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Proof step 5 from proof rmpos-get (previous step)

n < m, m ≤ # x0, 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] = (n < m ⊃ (a ' + x0)[n];x0[n]), x0 = []

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
n < m, m ≤ # x0, n < # x0, ∀ m0, n0. m0 < # x0 ∧ n0 + 1 < # x0 → (x0 -1l m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.rest[n0]) ⊦ x0 = [], ((a ' + x0) -1l m)[n] = (a ' + x0)[n], m = 0

Rule argument

Additional information

Used simplifier rules: fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic1