generic specification parameter elem using nat target sorts matrix; functions mkmatrix : nat × nat × elem → matrix; #r . : matrix → nat; #c . : matrix → nat; variables mx : matrix; r : nat; c : nat; a : elem; partial functions . [ . ] : matrix × nat × nat → elem with λ mx, r, c. r < #r mx ∧ c < #c mx; . [ . ] : matrix × nat × nat × elem → matrix with λ mx, r, c, a. r < #r mx ∧ c < #c mx; induction matrix generated by mkmatrix, [ ]; axioms extension: mx1 = mx2 ↔ #r mx1 = #r mx2 ∧ #c mx1 = #c mx2 ∧ (∀ r, c. r < #r mx1 ∧ c < #c mx1 → mx1[r, c] = mx2[r, c]); used for: ls; rowno-mkmatrix: #r mkmatrix(r, c, a) = r; used for: s, ls; colno-mkmatrix: #c mkmatrix(r, c, a) = c; used for: s, ls; get-mkmatrix: r < r0 ∧ c < c0 → mkmatrix(r0, c0, a)[r, c] = a; used for: s, ls; rowno-put: #r mx[r, c, a] = #r mx; used for: s, ls; colno-put: #c mx[r, c, a] = #c mx; used for: s, ls; put-same: r < #r mx ∧ c < #c mx → mx[r, c, a][r, c] = a; used for: s, ls, lc; put-otherrow: r ≠ r0 → mx[r, c, a][r0, c0] = mx[r0, c0]; used for: s, ls, lc; put-othercol: c ≠ c0 → mx[r, c, a][r0, c0] = mx[r0, c0]; used for: s, ls, lc; end generic specification