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Proof step 2 from proof same-size-append (previous step)

ar0 = ar1 + ar2 ⊦ # ar0 = # ar1 ↔ ar2 = mkarray(0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
⊦ #(ar0 + ar1) = # ar0 + # ar1
Proof step 4:
⊦ (ar + ar0) + ar1 = ar + ar0 + ar1
Proof step 5:
⊦ ar + mkarray(0) = ar

Rule argument

Additional information

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