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Proof step 14 from proof diffone-nodupsget (previous step)

n < # x0, a ∈ x0, ∀ a1, n0. a1 ∈ x0 ∧ n0 + 1 < # x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ pos(a, x0) < n, x0 = [], (a0 ' + (x0 \ a '))[n] = (¬ pos(a, x0) < n ⊃ (a0 ' + x0)[n];x0[n]), dups(x0), a0 ∈ x0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
n < # x0, a ∈ x0, n ≤ pos(a, x0), ∀ a1, n0. a1 ∈ x0 ∧ n0 + 1 < # x0 → (x0 \ a1 ')[n0] = (n0 < pos(a1, x0) ⊃ x0[n0];x0[n0 + 1]) ⊦ x0 = [], (a0 ' + (x0 \ a '))[n] = (a0 ' + x0)[n], dups(x0), a0 ∈ x0

Rule argument

Additional information

Used simplifier rules: lels: ⊦ ¬ m < n ↔ n ≤ m; from specification nat