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Proof step 14 from proof append-assoc (previous step)

⊦ (⌜x⌝ + ⌜x0⌝ ) + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];(n < # x0 + # x ⊃ x0[n - # x];nf(n - # x - # x0)))⌝

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝
Proof step 16:
⊦ ⌜x + x0⌝ + ⌜nf⌝ = ⌜λ n. (n < # x ⊃ x[n];(n < # x0 + # x ⊃ x0[n - # x];nf(n - # x - # x0)))⌝

Rule argument

spec: stream inst: name: append-finfin seq: ⊦ ⌜x + y⌝ = ⌜x⌝ + ⌜y⌝ subst: [y, x] → [x0, x] flags: rewrite, current

Additional information

Used terms: x0, x