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Proof step 5 from proof valid-indices-nonrec (previous step)

∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦ m ' + nx0 < # ar ↔ (∀ n. n = m ∨ n ∈ nx0 → n < # ar)

Heuristic cut applied rule cut formula

And obtained the following new goals

Proof step 6:
m ' + nx0 < # ar, ∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦ m ' + nx0 < # ar ↔ (∀ n. n = m ∨ n ∈ nx0 → n < # ar)
Proof step 10:
∀ ar. nx0 < # ar ↔ (∀ n. n ∈ nx0 → n < # ar) ⊦ m ' + nx0 < # ar ↔ (∀ n. n = m ∨ n ∈ nx0 → n < # ar), m ' + nx0 < # ar

Rule argument

fma: m ' + nx0 < # ar

Additional information

Used formulas: m ' + nx0 < # ar