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Proof step 25 from proof rmpos-in (previous step)

a ∈ (a0 ' + x0) -p n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ a = a0, x0 = [], dups(x0), a ∈ x0, a0 ∈ x0

User applied rule constructor cut

And obtained the following new goals

Proof step 26:
n = n1 +1, a ∈ (a0 ' + x0) -p n, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0) ⊦ a = a0, x0 = [], dups(x0), a0 ∈ x0, a ∈ x0

Rule argument

var: n

Additional information

Used simplifier rules: delpos-base: ⊦ (a ' + x) -p 0 = x;%nat freely generated by 0, +1;;%a: ⊦ (x + y) + z = x + y + z; from specification list