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Proof step 44 from proof correctness (previous step)

¬ m0 < m, C2[m0, n0] = 0, C.cols = B.cols, C.rows = A.rows, C4.cols = B.cols, C4.rows = A.rows, C2.cols = B.cols, C2.rows = A.rows, A.cols = B.rows, n0 < B.cols, m0 < A.rows, k0 < B.rows, m < A.rows, ∀ m1, n. m1 < A.rows ∧ n < B.cols → C2[m1, n] = (m1 < m ⊃ Σ(B.rows, λ k. A[m1, k] * B[k, n]);0), ∀ m0, n0. m0 < A.rows ∧ n0 < B.cols → C4[m0, n0] = C2[m0, n0] + (m0 = m ⊃ Σ(k0, λ k. A[m, k] * B[k, n0]);0), ∀ m1, n. m1 < A.rows ∧ n < B.cols → C[m1, n] = C4[m1, n] + (m1 = m ⊃ A[m, k0] * B[k0, n];0) ⊦ B.cols = 0, A.rows = 0, B.rows = 0, m0 = m, C[m0, n0] = C2[m0, n0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 45:
C2[m0, n0] = 0, C.cols = B.cols, C.rows = A.rows, C4.cols = B.cols, C4.rows = A.rows, C2.cols = B.cols, C2.rows = A.rows, A.cols = B.rows, m + 1 < A.rows, n0 < B.cols, m0 < A.rows, k0 < B.rows, m < m0, m < A.rows, ∀ m1, n. m1 < A.rows ∧ n < B.cols → C2[m1, n] = (m1 < m ⊃ Σ(B.rows, λ k. A[m1, k] * B[k, n]);0), ∀ m0, n0. m0 < A.rows ∧ n0 < B.cols → C4[m0, n0] = C2[m0, n0] + (m0 = m ⊃ Σ(k0, λ k. A[m, k] * B[k, n0]);0), ∀ m1, n. m1 < A.rows ∧ n < B.cols → C[m1, n] = C4[m1, n] + (m1 = m ⊃ A[m, k0] * B[k0, n];0) ⊦ B.cols = 0, A.rows = 0, B.rows = 0, m0 = m, C[m0, n0] = 0, m0 = 0

Rule argument

Additional information

Used simplifier rules: lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic1%succ: ⊦ m +1 = m + 1; from specification nat-basic2%trans-1: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification nat-basic1%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic1%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1%neq-01: ⊦ m ≠ n → (¬ m < n ↔ n < m); from specification nat-basic1