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Proof step 48 from proof correctness (previous step)

A.cols = B.rows, m2 = 0, C1 = A.rows × B.cols, m ≤ C2.rows, C2.rows = A.rows, C2.cols = B.cols, ∀ m0, n0. m0 < C2.rows ∧ n0 < C2.cols → C2[m0, n0] = C1[m0, n0] + (m0 < m ∧ n0 < C2.cols ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0), C2 = C0, m = m1, m < C2.rows, k1 = 0, k ≤ B.rows, C.rows = A.rows, C.cols = B.cols, ∀ m0, n0. m0 < C.rows ∧ n0 < C.cols → C[m0, n0] = C2[m0, n0] + (m0 = m ∧ n0 < C.cols ⊃ Σ(k, λ k. A[m0, k] * B[k, n0]);0), ¬ k < B.rows ⊦ ⟨m := m + 1⟩ ( ( m ≤ C.rows ∧ C.rows = A.rows ∧ C.cols = B.cols ∧ (∀ m0, n0. m0 < C.rows ∧ n0 < C.cols → C[m0, n0] = C1[m0, n0] + (m0 < m ∧ n0 < C.cols ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0))) ∧ C.rows - m < C0.rows - m1)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 49:
A.cols = B.rows, m2 = 0, C1 = A.rows × B.cols, m ≤ C2.rows, C2.rows = A.rows, C2.cols = B.cols, ∀ m0, n0. m0 < C2.rows ∧ n0 < C2.cols → C2[m0, n0] = C1[m0, n0] + (m0 < m ∧ n0 < C2.cols ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0), C2 = C0, m = m1, m < C2.rows, k1 = 0, k ≤ B.rows, C.rows = A.rows, C.cols = B.cols, ∀ m0, n0. m0 < C.rows ∧ n0 < C.cols → C[m0, n0] = C2[m0, n0] + (m0 = m ∧ n0 < C.cols ⊃ Σ(k, λ k. A[m0, k] * B[k, n0]);0), ¬ k < B.rows, ( ¬ m + 1 ≤ C.rows ∨ C.rows ≠ A.rows ∨ C.cols ≠ B.cols ∨ (∃ m0, n0. ¬(m0 < C.rows ∧ n0 < C.cols → C[m0, n0] = C1[m0, n0] + (m0 < m + 1 ∧ n0 < C.cols ⊃ Σ(B.rows, λ k. A[m0, k] * B[k, n0]);0)))) ∨ ¬ C.rows - m + 1 < C0.rows - m1 ⊦

Proof step 48 from proof correctness (previous step)

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Rule argument

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