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Proof step 11 from proof diffgetn-nodupssize (previous step)

n ≤ # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 \ x0[n0] ') = m ⊦ 1 + #(x0 \ (a ' + x0)[n] ') = # x0, a = (a ' + x0)[n], x0 = [], dups(x0), a ∈ 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:
n ≤ # x0, ∀ m, n0. # x0 = m + 1 ∧ n0 ≤ m → #(x0 \ x0[n0] ') = m ⊦ 1 + #(x0 \ x0[n - # a '] ') = # x0, a = x0[n - # a '], x0 = [], n < # a ', dups(x0), a ∈ x0

Rule argument

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

Additional information

Used simplifier rules: ⊦ n < # x → (x + y)[n] = x[n]; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ # a ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)% ⊦ a '[0] = a; (s) Used terms: n, x0, a '