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Proof step 12 from proof orderedle-all (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
(a0 ' + y)[n - 1] < (a ' + a0 ' + y)[m], ordered≤(a0 ' + y), m ≤ 1 + # y, n ≤ 1 + # y, m ≤ n, ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ n = 0, a0 < a

Rule argument

Additional information

Used simplifier rules: ⊦ n -1 = n - 1; (s)