Article GOBOARD8, MML version 4.99.1005

:: GOBOARD8:th 1
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 1 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3 + 1,b4) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4 + 2) or b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4) &
          b1 /. b2 = (GoB b1) *(b3 + 1,b4 + 2))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,b4)) + ((GoB b1) *(b3 + 1,b4 + 1))),(1 / 2) * (((GoB b1) *(b3,b4 + 1)) + ((GoB b1) *(b3 + 1,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 2
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3 + 2,b4 + 1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4 + 2) or b1 /. (b2 + 2) = (GoB b1) *(b3 + 2,b4 + 1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,b4 + 2))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,b4)) + ((GoB b1) *(b3 + 1,b4 + 1))),(1 / 2) * (((GoB b1) *(b3,b4 + 1)) + ((GoB b1) *(b3 + 1,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 3
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3 + 2,b4 + 1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4) or b1 /. (b2 + 2) = (GoB b1) *(b3 + 2,b4 + 1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,b4))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,b4)) + ((GoB b1) *(b3 + 1,b4 + 1))),(1 / 2) * (((GoB b1) *(b3,b4 + 1)) + ((GoB b1) *(b3 + 1,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 4
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 1 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3,b4) &
          b1 /. (b2 + 2) = (GoB b1) *(b3,b4 + 2) or b1 /. (b2 + 2) = (GoB b1) *(b3,b4) &
          b1 /. b2 = (GoB b1) *(b3,b4 + 2))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,b4)) + ((GoB b1) *(b3 + 1,b4 + 1))),(1 / 2) * (((GoB b1) *(b3,b4 + 1)) + ((GoB b1) *(b3 + 1,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 5
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3,b4 + 1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4 + 2) or b1 /. (b2 + 2) = (GoB b1) *(b3,b4 + 1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,b4 + 2))
   holds LSeg((1 / 2) * (((GoB b1) *(b3 + 1,b4)) + ((GoB b1) *(b3 + 2,b4 + 1))),(1 / 2) * (((GoB b1) *(b3 + 1,b4 + 1)) + ((GoB b1) *(b3 + 2,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 6
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         1 <= b4 &
         b4 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3,b4 + 1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,b4) or b1 /. (b2 + 2) = (GoB b1) *(b3,b4 + 1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,b4))
   holds LSeg((1 / 2) * (((GoB b1) *(b3 + 1,b4)) + ((GoB b1) *(b3 + 2,b4 + 1))),(1 / 2) * (((GoB b1) *(b3 + 1,b4 + 1)) + ((GoB b1) *(b3 + 2,b4 + 2)))) misses L~ b1;

:: GOBOARD8:th 7
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,1) &
         (b1 /. b2 = (GoB b1) *(b3 + 2,1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,2) or b1 /. (b2 + 2) = (GoB b1) *(b3 + 2,1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,2))
   holds LSeg(((1 / 2) * (((GoB b1) *(b3,1)) + ((GoB b1) *(b3 + 1,1)))) - |[0,1]|,(1 / 2) * (((GoB b1) *(b3,1)) + ((GoB b1) *(b3 + 1,2)))) misses L~ b1;

:: GOBOARD8:th 8
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,1) &
         (b1 /. b2 = (GoB b1) *(b3,1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,2) or b1 /. (b2 + 2) = (GoB b1) *(b3,1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,2))
   holds LSeg(((1 / 2) * (((GoB b1) *(b3 + 1,1)) + ((GoB b1) *(b3 + 2,1)))) - |[0,1]|,(1 / 2) * (((GoB b1) *(b3 + 1,1)) + ((GoB b1) *(b3 + 2,2)))) misses L~ b1;

:: GOBOARD8:th 9
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,width GoB b1) &
         (b1 /. b2 = (GoB b1) *(b3 + 2,width GoB b1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,(width GoB b1) -' 1) or b1 /. (b2 + 2) = (GoB b1) *(b3 + 2,width GoB b1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,(width GoB b1) -' 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,(width GoB b1) -' 1)) + ((GoB b1) *(b3 + 1,width GoB b1))),((1 / 2) * (((GoB b1) *(b3,width GoB b1)) + ((GoB b1) *(b3 + 1,width GoB b1)))) + |[0,1]|) misses L~ b1;

:: GOBOARD8:th 10
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,width GoB b1) &
         (b1 /. b2 = (GoB b1) *(b3,width GoB b1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 1,(width GoB b1) -' 1) or b1 /. (b2 + 2) = (GoB b1) *(b3,width GoB b1) &
          b1 /. b2 = (GoB b1) *(b3 + 1,(width GoB b1) -' 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b3 + 1,(width GoB b1) -' 1)) + ((GoB b1) *(b3 + 2,width GoB b1))),((1 / 2) * (((GoB b1) *(b3 + 1,width GoB b1)) + ((GoB b1) *(b3 + 2,width GoB b1)))) + |[0,1]|) misses L~ b1;

:: GOBOARD8:th 11
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b4 &
         b4 + 1 <= width GoB b1 &
         1 <= b3 &
         b3 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b3 + 1,b4 + 1) &
         (b1 /. b2 = (GoB b1) *(b3,b4 + 1) &
          b1 /. (b2 + 2) = (GoB b1) *(b3 + 2,b4 + 1) or b1 /. (b2 + 2) = (GoB b1) *(b3,b4 + 1) &
          b1 /. b2 = (GoB b1) *(b3 + 2,b4 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b3,b4)) + ((GoB b1) *(b3 + 1,b4 + 1))),(1 / 2) * (((GoB b1) *(b3 + 1,b4)) + ((GoB b1) *(b3 + 2,b4 + 1)))) misses L~ b1;

:: GOBOARD8:th 12
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         1 <= b4 &
         b4 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b4 + 1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(b4 + 1,b3 + 2) &
          b1 /. (b2 + 2) = (GoB b1) *(b4 + 2,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(b4 + 1,b3 + 2) &
          b1 /. b2 = (GoB b1) *(b4 + 2,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b4,b3)) + ((GoB b1) *(b4 + 1,b3 + 1))),(1 / 2) * (((GoB b1) *(b4 + 1,b3)) + ((GoB b1) *(b4 + 2,b3 + 1)))) misses L~ b1;

:: GOBOARD8:th 13
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         1 <= b4 &
         b4 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b4 + 1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(b4 + 1,b3 + 2) &
          b1 /. (b2 + 2) = (GoB b1) *(b4,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(b4 + 1,b3 + 2) &
          b1 /. b2 = (GoB b1) *(b4,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b4,b3)) + ((GoB b1) *(b4 + 1,b3 + 1))),(1 / 2) * (((GoB b1) *(b4 + 1,b3)) + ((GoB b1) *(b4 + 2,b3 + 1)))) misses L~ b1;

:: GOBOARD8:th 14
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 1 <= width GoB b1 &
         1 <= b4 &
         b4 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b4 + 1,b3) &
         (b1 /. b2 = (GoB b1) *(b4,b3) &
          b1 /. (b2 + 2) = (GoB b1) *(b4 + 2,b3) or b1 /. (b2 + 2) = (GoB b1) *(b4,b3) &
          b1 /. b2 = (GoB b1) *(b4 + 2,b3))
   holds LSeg((1 / 2) * (((GoB b1) *(b4,b3)) + ((GoB b1) *(b4 + 1,b3 + 1))),(1 / 2) * (((GoB b1) *(b4 + 1,b3)) + ((GoB b1) *(b4 + 2,b3 + 1)))) misses L~ b1;

:: GOBOARD8:th 15
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         1 <= b4 &
         b4 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b4 + 1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(b4 + 1,b3) &
          b1 /. (b2 + 2) = (GoB b1) *(b4 + 2,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(b4 + 1,b3) &
          b1 /. b2 = (GoB b1) *(b4 + 2,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b4,b3 + 1)) + ((GoB b1) *(b4 + 1,b3 + 2))),(1 / 2) * (((GoB b1) *(b4 + 1,b3 + 1)) + ((GoB b1) *(b4 + 2,b3 + 2)))) misses L~ b1;

:: GOBOARD8:th 16
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3, b4 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         1 <= b4 &
         b4 + 2 <= len GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(b4 + 1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(b4 + 1,b3) &
          b1 /. (b2 + 2) = (GoB b1) *(b4,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(b4 + 1,b3) &
          b1 /. b2 = (GoB b1) *(b4,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *(b4,b3 + 1)) + ((GoB b1) *(b4 + 1,b3 + 2))),(1 / 2) * (((GoB b1) *(b4 + 1,b3 + 1)) + ((GoB b1) *(b4 + 2,b3 + 2)))) misses L~ b1;

:: GOBOARD8:th 17
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(1,b3 + 2) &
          b1 /. (b2 + 2) = (GoB b1) *(2,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(1,b3 + 2) &
          b1 /. b2 = (GoB b1) *(2,b3 + 1))
   holds LSeg(((1 / 2) * (((GoB b1) *(1,b3)) + ((GoB b1) *(1,b3 + 1)))) - |[1,0]|,(1 / 2) * (((GoB b1) *(1,b3)) + ((GoB b1) *(2,b3 + 1)))) misses L~ b1;

:: GOBOARD8:th 18
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(1,b3) &
          b1 /. (b2 + 2) = (GoB b1) *(2,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(1,b3) &
          b1 /. b2 = (GoB b1) *(2,b3 + 1))
   holds LSeg(((1 / 2) * (((GoB b1) *(1,b3 + 1)) + ((GoB b1) *(1,b3 + 2)))) - |[1,0]|,(1 / 2) * (((GoB b1) *(1,b3 + 1)) + ((GoB b1) *(2,b3 + 2)))) misses L~ b1;

:: GOBOARD8:th 19
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(len GoB b1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(len GoB b1,b3 + 2) &
          b1 /. (b2 + 2) = (GoB b1) *((len GoB b1) -' 1,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(len GoB b1,b3 + 2) &
          b1 /. b2 = (GoB b1) *((len GoB b1) -' 1,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *((len GoB b1) -' 1,b3)) + ((GoB b1) *(len GoB b1,b3 + 1))),((1 / 2) * (((GoB b1) *(len GoB b1,b3)) + ((GoB b1) *(len GoB b1,b3 + 1)))) + |[1,0]|) misses L~ b1;

:: GOBOARD8:th 20
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
   st 1 <= b2 & b2 + 2 <= len b1
for b3 being Element of NAT
      st 1 <= b3 &
         b3 + 2 <= width GoB b1 &
         b1 /. (b2 + 1) = (GoB b1) *(len GoB b1,b3 + 1) &
         (b1 /. b2 = (GoB b1) *(len GoB b1,b3) &
          b1 /. (b2 + 2) = (GoB b1) *((len GoB b1) -' 1,b3 + 1) or b1 /. (b2 + 2) = (GoB b1) *(len GoB b1,b3) &
          b1 /. b2 = (GoB b1) *((len GoB b1) -' 1,b3 + 1))
   holds LSeg((1 / 2) * (((GoB b1) *((len GoB b1) -' 1,b3 + 1)) + ((GoB b1) *(len GoB b1,b3 + 2))),((1 / 2) * (((GoB b1) *(len GoB b1,b3 + 1)) + ((GoB b1) *(len GoB b1,b3 + 2)))) + |[1,0]|) misses L~ b1;

:: GOBOARD8:th 21
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of bool the carrier of TOP-REAL 2
      st for b3 being Element of the carrier of TOP-REAL 2
              st b3 in b2
           holds b3 `1 < ((GoB b1) *(1,1)) `1
   holds b2 misses L~ b1;

:: GOBOARD8:th 22
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of bool the carrier of TOP-REAL 2
      st for b3 being Element of the carrier of TOP-REAL 2
              st b3 in b2
           holds ((GoB b1) *(len GoB b1,1)) `1 < b3 `1
   holds b2 misses L~ b1;

:: GOBOARD8:th 23
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of bool the carrier of TOP-REAL 2
      st for b3 being Element of the carrier of TOP-REAL 2
              st b3 in b2
           holds b3 `2 < ((GoB b1) *(1,1)) `2
   holds b2 misses L~ b1;

:: GOBOARD8:th 24
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of bool the carrier of TOP-REAL 2
      st for b3 being Element of the carrier of TOP-REAL 2
              st b3 in b2
           holds ((GoB b1) *(1,width GoB b1)) `2 < b3 `2
   holds b2 misses L~ b1;

:: GOBOARD8:th 25
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
      st 1 <= b2 & b2 + 2 <= len GoB b1
   holds LSeg(((1 / 2) * (((GoB b1) *(b2,1)) + ((GoB b1) *(b2 + 1,1)))) - |[0,1]|,((1 / 2) * (((GoB b1) *(b2 + 1,1)) + ((GoB b1) *(b2 + 2,1)))) - |[0,1]|) misses L~ b1;

:: GOBOARD8:th 26
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((GoB b1) *(1,1)) - |[1,1]|,((1 / 2) * (((GoB b1) *(1,1)) + ((GoB b1) *(2,1)))) - |[0,1]|) misses L~ b1;

:: GOBOARD8:th 27
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((1 / 2) * (((GoB b1) *((len GoB b1) -' 1,1)) + ((GoB b1) *(len GoB b1,1)))) - |[0,1]|,((GoB b1) *(len GoB b1,1)) + |[1,- 1]|) misses L~ b1;

:: GOBOARD8:th 28
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
      st 1 <= b2 & b2 + 2 <= len GoB b1
   holds LSeg(((1 / 2) * (((GoB b1) *(b2,width GoB b1)) + ((GoB b1) *(b2 + 1,width GoB b1)))) + |[0,1]|,((1 / 2) * (((GoB b1) *(b2 + 1,width GoB b1)) + ((GoB b1) *(b2 + 2,width GoB b1)))) + |[0,1]|) misses L~ b1;

:: GOBOARD8:th 29
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((GoB b1) *(1,width GoB b1)) + |[- 1,1]|,((1 / 2) * (((GoB b1) *(1,width GoB b1)) + ((GoB b1) *(2,width GoB b1)))) + |[0,1]|) misses L~ b1;

:: GOBOARD8:th 30
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((1 / 2) * (((GoB b1) *((len GoB b1) -' 1,width GoB b1)) + ((GoB b1) *(len GoB b1,width GoB b1)))) + |[0,1]|,((GoB b1) *(len GoB b1,width GoB b1)) + |[1,1]|) misses L~ b1;

:: GOBOARD8:th 31
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
      st 1 <= b2 & b2 + 2 <= width GoB b1
   holds LSeg(((1 / 2) * (((GoB b1) *(1,b2)) + ((GoB b1) *(1,b2 + 1)))) - |[1,0]|,((1 / 2) * (((GoB b1) *(1,b2 + 1)) + ((GoB b1) *(1,b2 + 2)))) - |[1,0]|) misses L~ b1;

:: GOBOARD8:th 32
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((GoB b1) *(1,1)) - |[1,1]|,((1 / 2) * (((GoB b1) *(1,1)) + ((GoB b1) *(1,2)))) - |[1,0]|) misses L~ b1;

:: GOBOARD8:th 33
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((1 / 2) * (((GoB b1) *(1,(width GoB b1) -' 1)) + ((GoB b1) *(1,width GoB b1)))) - |[1,0]|,((GoB b1) *(1,width GoB b1)) + |[- 1,1]|) misses L~ b1;

:: GOBOARD8:th 34
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
for b2 being Element of NAT
      st 1 <= b2 & b2 + 2 <= width GoB b1
   holds LSeg(((1 / 2) * (((GoB b1) *(len GoB b1,b2)) + ((GoB b1) *(len GoB b1,b2 + 1)))) + |[1,0]|,((1 / 2) * (((GoB b1) *(len GoB b1,b2 + 1)) + ((GoB b1) *(len GoB b1,b2 + 2)))) + |[1,0]|) misses L~ b1;

:: GOBOARD8:th 35
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((GoB b1) *(len GoB b1,1)) + |[1,- 1]|,((1 / 2) * (((GoB b1) *(len GoB b1,1)) + ((GoB b1) *(len GoB b1,2)))) + |[1,0]|) misses L~ b1;

:: GOBOARD8:th 36
theorem
for b1 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2 holds
   LSeg(((1 / 2) * (((GoB b1) *(len GoB b1,(width GoB b1) -' 1)) + ((GoB b1) *(len GoB b1,width GoB b1)))) + |[1,0]|,((GoB b1) *(len GoB b1,width GoB b1)) + |[1,1]|) misses L~ b1;

:: GOBOARD8:th 37
theorem
for b1 being Element of NAT
for b2 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
      st 1 <= b1 & b1 + 1 <= len b2
   holds Int left_cell(b2,b1) misses L~ b2;

:: GOBOARD8:th 38
theorem
for b1 being Element of NAT
for b2 being non constant non empty circular special unfolded s.c.c. standard FinSequence of the carrier of TOP-REAL 2
      st 1 <= b1 & b1 + 1 <= len b2
   holds Int right_cell(b2,b1) misses L~ b2;