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Proof step 3 from proof append-zero-left (previous step)

⊦ #(mkarray(0) + ar) = # ar ∧ (∀ n. n < #(mkarray(0) + ar) → (mkarray(0) + ar)[n] = ar[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ #(ar0 + ar1) = # ar0 + # ar1
Proof step 5:
⊦ (ar + ar0) + ar1 = ar + ar0 + ar1
Proof step 6:
n < # ar ⊦ (mkarray(0) + ar)[n] = ar[n]

Rule argument

Additional information

Used simplifier rules: append-len: ⊦ #(ar0 + ar1) = # ar0 + # ar1;%append-a: ⊦ (ar + ar0) + ar1 = ar + ar0 + ar1;% ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ # mkarray(n) = n; (s)