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Proof step 4 from proof pos-get (previous step)

n ≤ # x0, ∀ n0. n0 < # x0 → pos(x0[n0], x0) = n0 ∨ x0 = [] ⊦ pos((a ' + x0)[n], a ' + x0) = n, a ∈ x0, dups(x0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 6:
¬ n < # a ', n ≤ # x0, ∀ n0. n0 < # x0 → pos(x0[n0], x0) = n0 ∨ x0 = [] ⊦ pos(x0[n - # a '], a ' + x0) = n, a ∈ x0, dups(x0)

Rule argument

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

Additional information

Used simplifier rules: get-zero-01: ⊦ (a ' + x)[0] = a;%pos-y: ⊦ pos(a, a ' + x) = 0;%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, a '