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Proof step 4 from proof dot-assoc (previous step)

A.cols = B.rows, B.cols = C.rows ⊦ ((A * B) * C).rows = (A * B * C).rows ∧ ((A * B) * C).cols = (A * B * C).cols ∧ (∀ m, n. m < ((A * B) * C).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 5:
A.cols = B.rows, B.cols = C.rows ⊦ ((A * B) * C).rows = (A * B * C).rows ∧ ((A * B) * C).cols = (A * B * C).cols ∧ (m < ((A * B) * C).rows ∧ n < ((A * B) * C).cols → ((A * B) * C)[m, n] = (A * B * C)[m, n])

Proof step 4 from proof dot-assoc (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information