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Proof step 2 from proof put-both-eq (previous step)

⊦ ar[n, a] = ar[n, b] ↔ n < # ar → a = b

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:
⊦ # ar[n, a] = # ar[n, b] ∧ (∀ n0. n0 < # ar[n, a] → ar[n, a][n0] = ar[n, b][n0]) ↔ n < # ar → a = b

Rule argument

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

Additional information

Used terms: ar[n, b], ar[n, a]