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Proof step 12 from proof cons-eq (previous step)

(0 < # a ' ⊃ a '[0];nf(0 - # a ')) = (0 < # a0 ' ⊃ a0 '[0];nf0(0 - # a0 ')), (λ n. (n < # a ' ⊃ a '[n];nf(n - # a '))) = (λ n. (n < # a0 ' ⊃ a0 '[n];nf0(n - # a0 '))) ⊦ a = a0 ∧ ⌜nf⌝ = ⌜nf0⌝

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(λ n. (n = 0 ⊃ a0;nf(n - 1))) = (λ n. (n = 0 ⊃ a0;nf0(n - 1))) ⊦ nf = nf0

Rule argument

Additional information

Used simplifier rules: inj-01: ⊦ ⌜nf⌝ = ⌜nf0⌝ ↔ nf = nf0; from specification stream-basic%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%one-03: ⊦ a '[0] = a; from specification list-del%len-02: ⊦ # a ' = 0 +1; from specification list