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Proof step 9 from proof rmpos-get (previous step)

m1 < # x0, n < # x0, n ≤ m1, ∀ n0, m0. n0 + 1 < # x0 ∧ m0 < # x0 → (x0 -p m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.tail[n0]) ⊦ (a ' + (x0 -p m1))[n] = (a ' + x0)[n], x0 = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 10:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 11:
n < # x0, m1 < # x0, n ≤ m1, ∀ n0, m0. n0 + 1 < # x0 ∧ m0 < # x0 → (x0 -p m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.tail[n0]) ⊦ (x0 -p m1)[n - # a '] = (a ' + x0)[n], x0 = [], n < # a '

Rule argument

spec: <toplevel> name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [n, x0 -p m1, a '] flags: <all paths>

Additional information

Used simplifier rules: get-zero-01: ⊦ (a ' + x)[0] = a;% ⊦ # a ' = 0 +1; (s)% ⊦ m < 1 ↔ m = 0; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%a: ⊦ (x + y) + z = x + y + z; from specification list Used terms: n, x0 -p m1, a '