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Proof step 9 from proof expand-cons (previous step)

⊦ ⌜nf⌝ = ⌜nf(0) '⌝ + ⌜λ n. nf(n + 1)⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ⌜a '⌝ + ⌜nf⌝ = ⌜λ n. (n = 0 ⊃ a;nf(n -1))⌝
Proof step 11:
⊦ ⌜nf⌝ = ⌜λ n. (n = 0 ⊃ nf(0);nf(n -1 + 1))⌝

Rule argument

spec: stream inst: name: one-inf seq: ⊦ ⌜a '⌝ + ⌜nf⌝ = ⌜λ n. (n = 0 ⊃ a;nf(n -1))⌝ subst: [nf, a] → [λ n. nf(n + 1), nf(0)] flags: rewrite, current

Additional information

Used terms: λ n. nf(n + 1), nf(0)