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Proof step 2 from proof dot-assoc (previous step)

A.cols = B.rows, B.cols = C.rows ⊦ (A * B) * C = A * B * C

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ A = B ↔ A.rows = B.rows ∧ A.cols = B.cols ∧ (∀ m, n. m < A.rows ∧ n < A.cols → A[m, n] = B[m, n])
Proof step 4:
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])

Rule argument

spec: matrix inst: name: ext seq: ⊦ A = B ↔ A.rows = B.rows ∧ A.cols = B.cols ∧ (∀ m, n. m < A.rows ∧ n < A.cols → A[m, n] = B[m, n]) subst: [B, A] → [A * B * C, (A * B) * C] flags: rewrite

Additional information

Used terms: A * B * C, (A * B) * C