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Proof step 6 from proof ex-smallest-notin (previous step)

∀ n0, ns. n0 < n → true → n0 ∈ ns ∨ (∃ n. ¬ n ∈ ns ∧ (∀ m. ¬ m ∈ ns → n ≤ m)) ⊦ n ∈ ns, ∃ n. ¬ n ∈ ns ∧ (∀ m. ¬ m ∈ ns → n ≤ m)

User applied rule exists right

And obtained the following new goals

Proof step 7:
∀ n0, ns. n0 < n → true → n0 ∈ ns ∨ (∃ n. ¬ n ∈ ns ∧ (∀ m. ¬ m ∈ ns → n ≤ m)) ⊦ n ∈ ns, ∃ n. ¬ n ∈ ns ∧ (∀ m. ¬ m ∈ ns → n ≤ m), ¬ n ∈ ns ∧ (∀ m. ¬ m ∈ ns → n ≤ m)

Rule argument

pos: right 2 terms: n abort: F discard: F computed: T

Additional information

Used terms: n