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Proof step 1 from proof idexcept-extract-left (conclusion)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

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

Rule argument

Additional information

Used simplifier rules: Idexcept: ⊦ id○(ar0, ar1, n) ↔ ¬ ¬(# ar0 = # ar1 ∧ (∀ m. m < # ar0 ∧ m ≠ n → ar0[m] = ar1[m]));