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Proof step 17 from proof rmpos-get (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
m < # x0, n < # x0, m ≤ n, ∀ n0, m0. n0 + 1 < # x0 ∧ m0 < # x0 → (x0 -p m0)[n0] = (n0 < m0 ⊃ x0[n0];x0.tail[n0]) ⊦ ((a ' + x0) -p m)[n] = x0[n], x0 = []

Rule argument

Additional information

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