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Proof step 28 from proof rmpos-in (previous step)

n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0), a = a0 ∨ a ∈ x0 ⊦ x0 = [], a = (a0 ' + x0)[n], a ∈ (a0 ' + x0) -1l n, a0 ∈ x0, dups(x0)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 29:
a ∈ x0, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0), a = a0 ∨ a ∈ x0 ⊦ x0 = [], a = (a0 ' + x0)[n], a ∈ (a0 ' + x0) -1l n, a0 ∈ x0, dups(x0)
Proof step 36:
n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -1l n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0), a = a0 ∨ a ∈ x0 ⊦ a ∈ x0, x0 = [], a = (a0 ' + x0)[n], a ∈ (a0 ' + x0) -1l n, a0 ∈ x0, dups(x0)

Rule argument

fma: a ∈ x0

Additional information

Used formulas: a ∈ x0