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Proof step 11 from proof rmpos-in (previous step)

a0 = (a0 ' + x0)[n], a0 ∈ (a0 ' + x0) -p n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p 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 12:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 13:
a0 = x0[n - # a0 '], a0 ∈ (a0 ' + x0) -p n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ x0 = [], n < # a0 ', dups(x0), a0 ∈ x0

Rule argument

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

Additional information

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