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Proof step 12 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]) ⊦ (x0 -p m1)[n - 1] = (a ' + x0)[n], n = 0, x0 = []

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
n = m + 1, 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)[m] = (a ' + x0)[n], n = 0, x0 = []

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m