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Proof step 6 from proof ext-rec (previous step)

# ar0 = # ar1, ∀ m. m < # ar1 → ar1[m] = (n = m ⊃ a;ar0[m]) ⊦ ar1 = ar0[n, a]

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ar1 = ar2 ↔ # ar1 = # ar2 ∧ (∀ n. n < # ar1 → ar1[n] = ar2[n])
Proof step 8:
# ar0 = # ar1, ∀ m. m < # ar1 → ar1[m] = (n = m ⊃ a;ar0[m]) ⊦ # ar1 = # ar0[n, a] ∧ (∀ n0. n0 < # ar1 → ar1[n0] = ar0[n, a][n0])

Rule argument

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

Additional information

Used terms: ar0[n, a], ar1