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Proof step 1 from proof idexcept-write-at0 (conclusion)

⊦ id○(ar0[n, a], ar1, n) ↔ id○(ar0, ar1, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 2:
# ar0 = # ar1, m < # ar1, ∀ m. m < # ar1 ∧ m ≠ n → ar0[m] = ar1[m] ⊦ ar0[m] = ar1[m], m = n

Rule argument

Additional information

Used simplifier rules: Idexcept: ⊦ id○(ar0, ar1, n) ↔ # ar0 = # ar1 ∧ (∀ m. m < # ar0 ∧ m ≠ n → ar0[m] = ar1[m]);% ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ m ≠ n → ar[n, a][m] = ar[m]; (s)% ⊦ # ar[n, a] = # ar; (s)