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Proof step 17 from proof orderedle-all (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
(a0 ' + y)[m0] < a, ordered≤(a0 ' + y), m0 ≤ # y, ∀ m, n. m ≤ n ∧ n < 1 + # y → ¬ (a0 ' + y)[n] < (a0 ' + y)[m] ⊦ a0 < a

Rule argument

Additional information

Used simplifier rules: a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ (a ' + x)[0] = a; (s)% ⊦ 0 ≤ m; (s)