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

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0
Proof step 11:
(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-basic inst: name: inj-01 seq: ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0 subst: [nf0, nf] → [λ n. (n < # a0 ' ⊃ a0 '[n];nf0(n - # a0 ')), λ n. (n < # a ' ⊃ a '[n];nf(n - # a '))] flags: rewrite

Additional information

Used terms: λ n. (n < # a0 ' ⊃ a0 '[n];nf0(n - # a0 ')), λ n. (n < # a ' ⊃ a '[n];nf(n - # a '))