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Proof step 29 from proof rmpos-in (previous step)

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

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 30:
a ∈ x0, n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0), a = a0 ∨ a ∈ x0 ⊦ a = (a0 ' + x0)[n], x0 = [], dups(x0), a0 ∈ x0, a ∈ (a0 ' + x0) -p n
Proof step 37:
n ≤ # x0, ∀ n0, a1. n0 < # x0 → (a1 ∈ x0 -p n0 ↔ a1 ≠ x0[n0] ∧ a1 ∈ x0), a = a0 ∨ a ∈ x0 ⊦ a = (a0 ' + x0)[n], x0 = [], dups(x0), a0 ∈ x0, a ∈ (a0 ' + x0) -p n, a ∈ x0

Rule argument

fma: a ∈ x0

Additional information

Used formulas: a ∈ x0