let i, j, k be Nat; for f being FinSequence of (TOP-REAL 2)
for G being Go-board st 1 <= k & k + 1 <= len f & f is_sequence_on G & [i,j] in Indices G & [(i + 1),j] in Indices G & f /. k = G * (i,j) & f /. (k + 1) = G * ((i + 1),j) holds
left_cell (f,k,G) = cell (G,i,j)
let f be FinSequence of (TOP-REAL 2); for G being Go-board st 1 <= k & k + 1 <= len f & f is_sequence_on G & [i,j] in Indices G & [(i + 1),j] in Indices G & f /. k = G * (i,j) & f /. (k + 1) = G * ((i + 1),j) holds
left_cell (f,k,G) = cell (G,i,j)
let G be Go-board; ( 1 <= k & k + 1 <= len f & f is_sequence_on G & [i,j] in Indices G & [(i + 1),j] in Indices G & f /. k = G * (i,j) & f /. (k + 1) = G * ((i + 1),j) implies left_cell (f,k,G) = cell (G,i,j) )
A1:
( i < i + 1 & i + 1 <= (i + 1) + 1 )
by XREAL_1:29;
assume
( 1 <= k & k + 1 <= len f & f is_sequence_on G & [i,j] in Indices G & [(i + 1),j] in Indices G & f /. k = G * (i,j) & f /. (k + 1) = G * ((i + 1),j) )
; left_cell (f,k,G) = cell (G,i,j)
hence
left_cell (f,k,G) = cell (G,i,j)
by A1, Def2; verum