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Proof step 51 from proof correctness (previous step)

¬ m1 < m, A.cols = B.rows, C0.rows = A.rows, C0.cols = B.cols, C.rows = A.rows, C.cols = B.cols, n < B.cols, m < A.rows, m1 < A.rows, ∀ m0, n0. m0 < A.rows ∧ n0 < B.cols → C0[m0, n0] = (m0 < m1 ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0), ∀ m, n. m < A.rows ∧ n < B.cols → C[m, n] = C0[m, n] + (m = m1 ⊃ Σ(B.rows, λ k. A[m1, k] * B[k, n]);0) ⊦ C[m, n] = Σ(B.rows, λ k. A[m, k] * B[k, n]), B.cols = 0, A.rows = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 52:
A.cols = B.rows, C0.rows = A.rows, C0.cols = B.cols, C.rows = A.rows, C.cols = B.cols, n < B.cols, m1 < A.rows, m ≤ m1, m < A.rows, ∀ m0, n0. m0 < A.rows ∧ n0 < B.cols → C0[m0, n0] = (m0 < m1 ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0), ∀ m, n. m < A.rows ∧ n < B.cols → C[m, n] = C0[m, n] + (m = m1 ⊃ Σ(B.rows, λ k. A[m1, k] * B[k, n]);0) ⊦ C[m, n] = Σ(B.rows, λ k. A[m, k] * B[k, n]), B.cols = 0, A.rows = 0

Rule argument

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat