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Proof step 14 from proof rmpos-get (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
m < # x0, m ≤ n, n < # x0, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.rest[n0]) ⊦ ((a ' + x0) -1l m)[n] = x0[n], x0 = []

Rule argument

Additional information

Used simplifier rules: lels-03: ⊦ m < n → m ≤ n; from specification nat%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat