Article GOBOARD3, MML version 4.99.1005

:: GOBOARD3:th 1
theorem
for b1 being FinSequence of the carrier of TOP-REAL 2
for b2 being non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of (the carrier of TOP-REAL 2) *
      st (for b3 being Element of NAT
               st b3 in dom b1
            holds ex b4, b5 being Element of NAT st
               [b4,b5] in Indices b2 & b1 /. b3 = b2 *(b4,b5)) &
         b1 is one-to-one &
         b1 is unfolded &
         b1 is s.n.c. &
         b1 is special
   holds ex b3 being FinSequence of the carrier of TOP-REAL 2 st
      b3 is_sequence_on b2 & b3 is one-to-one & b3 is unfolded & b3 is s.n.c. & b3 is special & L~ b1 = L~ b3 & b1 /. 1 = b3 /. 1 & b1 /. len b1 = b3 /. len b3 & len b1 <= len b3;

:: GOBOARD3:th 2
theorem
for b1 being FinSequence of the carrier of TOP-REAL 2
for b2 being non empty-yielding tabular X_equal-in-line Y_equal-in-column Y_increasing-in-line X_increasing-in-column FinSequence of (the carrier of TOP-REAL 2) *
      st (for b3 being Element of NAT
               st b3 in dom b1
            holds ex b4, b5 being Element of NAT st
               [b4,b5] in Indices b2 & b1 /. b3 = b2 *(b4,b5)) &
         b1 is being_S-Seq
   holds ex b3 being FinSequence of the carrier of TOP-REAL 2 st
      b3 is_sequence_on b2 & b3 is being_S-Seq & L~ b1 = L~ b3 & b1 /. 1 = b3 /. 1 & b1 /. len b1 = b3 /. len b3 & len b1 <= len b3;