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Proof step 7 from proof cons-eq (previous step)

⌜λ n. (n < # a ' ⊃ a '[n];nf(n - # a '))⌝ = ⌜a0 '⌝ + ⌜nf0⌝ ⊦ a = a0 ∧ ⌜nf⌝ = ⌜nf0⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ ⌜x⌝ + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];nf(n - # x))⌝
Proof step 9:
⌜λ n. (n < # a ' ⊃ a '[n];nf(n - # a '))⌝ = ⌜λ n. (n < # a0 ' ⊃ a0 '[n];nf0(n - # a0 '))⌝ ⊦ a = a0 ∧ ⌜nf⌝ = ⌜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 '