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Proof step 6 from proof append-cancel-l (previous step)

⌜x⌝ + ⌜nf⌝ = ⌜x⌝ + ⌜nf0⌝ ⊦ nf = nf0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ⌜x⌝ + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];nf(n - # x))⌝
Proof step 8:
⌜λ n. (n < # x ⊃ x[n];nf(n - # x))⌝ = ⌜x⌝ + ⌜nf0⌝ ⊦ 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] → [nf, x] flags: rewrite, current

Additional information

Used terms: nf, x