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Proof step 2 from proof idexcept-extract-right (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 4:
⊦ # ar0 = # ar1 ∧ (∀ m. m < # ar0 ∧ m ≠ n → ar0[m] = ar1[m]) ↔ # ar1 = # ar0[n, ar1[n]] ∧ (∀ n0. n0 < # ar1 → ar1[n0] = ar0[n, ar1[n]][n0])

Rule argument

spec: array inst: name: Extension seq: ⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n]) subst: [ar2, ar1] → [ar0[n, ar1[n]], ar1] flags: rewrite

Additional information

Used terms: ar0[n, ar1[n]], ar1