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Proof step 4 from proof cons-eq-inf (previous step)

⊦ ⌜nf⌝ = ⌜a0 '⌝ + ⌜nf0⌝ ↔ nf(0) = a0 ∧ (λ n. nf(n + 1)) = nf0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ⌜x⌝ + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];nf(n - # x))⌝
Proof step 6:
⊦ ⌜nf⌝ = ⌜λ n. (n < # a0 ' ⊃ a0 '[n];nf0(n - # a0 '))⌝ ↔ nf(0) = a0 ∧ (λ n. nf(n + 1)) = nf0

Rule argument

spec: stream inst: name: append-fininf seq: ⊦ ⌜x⌝ + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];nf(n - # x))⌝ subst: [nf, x] → [nf0, a0 '] flags: rewrite, current

Additional information

Used terms: nf0, a0 '