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\wedge 0 \leq j < SIZE : \newline +$\exists (i, j: \mathbb{N} ~|~ 0 \leq i < SIZE \wedge 0 \leq j < SIZE : \newline ~\qquad \mbox{checkHoriz}(i, j) \lor \mbox{checkVert}(i, j) \lor \mbox{checkDiag}(i, j))$\\ \noindent{\bf local functions}\\ @@ -18,13 +18,13 @@ $\mbox{checkHoriz}(i, j) \equiv (\newline ~\qquad i + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i+1][j] \land board[i][j] = board[i+2][j] \newline )$\\[\baselineskip] -checkHoriz: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ -$\mbox{checkHoriz}(i, j) \equiv (\newline +checkVert: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ +$\mbox{checkVert}(i, j) \equiv (\newline ~\qquad j + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i][j+1] \land board[i][j] = board[i][j+2] \newline )$\\[\baselineskip] checkDiag: $\mathbb{N} \times \mathbb{N} \rightarrow \mathbb{B}$\\ -$\mbox{checkHoriz}(i, j) \equiv (\newline +$\mbox{checkDiag}(i, j) \equiv (\newline ~\qquad i + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad j + 2 \geq SIZE \Rightarrow \mbox{false} ~|\newline ~\qquad \mbox{true} \Rightarrow board[i][j] = board[i+1][j+1] \land board[i][j] = board[i+2][j+2] \newline -- GitLab