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Proof step 1 from proof cputput (conclusion)

m < # ar ⊦ ar[m, a][m, b] = ar[m, b]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 3:
m < # ar ⊦ # ar[m, a][m, b] = # ar[m, b] ∧ (∀ n. n < # ar[m, a][m, b] → ar[m, a][m, b][n] = ar[m, b][n])

Rule argument

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

Additional information

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