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Proof step 10 from proof dot-assoc (previous step)

A.cols = (B * C).rows, A.cols = B.rows, B.cols = C.rows ⊦ A.rows = A.rows ∧ ((A * B) * C).cols = (A * B * C).cols ∧ (m < A.rows ∧ n < ((A * B) * C).cols → ((A * B) * C)[m, n] = (A * B * C)[m, n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
A.cols = B.rows, B.cols = C.rows ⊦ ((A * B) * C).cols = (A * B * C).cols ∧ (m < A.rows ∧ n < ((A * B) * C).cols → ((A * B) * C)[m, n] = (A * B * C)[m, n])

Rule argument

Additional information

Used simplifier rules: rows-dot: ⊦ A.cols = B.rows → (A * B).rows = A.rows;