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Proof step 13 from proof orderedle-all (previous step)

m ≤ 1 + # y, n ≤ 1 + # y, ordered≤(a0 ' + y), m ≤ n, (a0 ' + y)[n - 1] < (a ' + a0 ' + y)[m], ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ n = 0, a0 < a

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 14:
n = m0 + 1, m ≤ 1 + # y, n ≤ 1 + # y, ordered≤(a0 ' + y), m ≤ n, (a0 ' + y)[m0] < (a ' + a0 ' + y)[m], ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ n = 0, a0 < a

Rule argument

spec: nat inst: name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m0] flags:

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m0