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Proof step 17 from proof rmpos-in (previous step)

n ≤ # x0, (a0 ' + x0)[n] ∈ (a0 ' + x0) -1l n, (a0 ' + x0)[n] ∈ x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], dups(x0), a0 ∈ x0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 19:
¬ n < # a0 ', n ≤ # x0, x0[n - # a0 '] ∈ (a0 ' + x0) -1l n, x0[n - # a0 '] ∈ x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], dups(x0), a0 ∈ x0

Rule argument

spec: inst: name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [n, x0, a0 '] flags: rewrite, current

Additional information

Used simplifier rules: get-zero-01: ⊦ (a ' + x)[0] = a;%len-02: ⊦ # a ' = 0 +1; from specification list%one-01: ⊦ m < 1 ↔ m = 0; from specification nat-basic1%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: n, x0, a0 '