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Proof step 4 from proof append-eq-emptyar (previous step)

ar0 + ar1 = mkarray(0) ⊦ ar0 = mkarray(0) ∧ ar1 = mkarray(0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [mkarray(0), ar0 + ar1] flags: <all paths>

Additional information

Used simplifier rules: append-len: ⊦ #(ar0 + ar1) = # ar0 + # ar1;%append-a: ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1;% ⊦ # mkarray(n) = n; (s)% ⊦ m + n = 0 ↔ m = 0 ∧ n = 0; (ws)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # ar = 0 → (mkarray(0) = ar ↔ true); (ss) Used terms: mkarray(0), ar0 + ar1