let i, j, k be Nat; :: thesis: 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 + 1),j) & f /. (k + 1) = G * (i,j) holds
front_left_cell (f,k,G) = cell (G,(i -' 1),(j -' 1))
let f be FinSequence of (TOP-REAL 2); :: thesis: 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 + 1),j) & f /. (k + 1) = G * (i,j) holds
front_left_cell (f,k,G) = cell (G,(i -' 1),(j -' 1))
let G be Go-board; :: thesis: ( 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 + 1),j) & f /. (k + 1) = G * (i,j) implies front_left_cell (f,k,G) = cell (G,(i -' 1),(j -' 1)) )
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 + 1),j) & f /. (k + 1) = G * (i,j) ) ; :: thesis: front_left_cell (f,k,G) = cell (G,(i -' 1),(j -' 1))
hence front_left_cell (f,k,G) = cell (G,(i -' 1),(j -' 1)) by A1, Def4; :: thesis: verum