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Proof step 7 from proof below-rem-in (previous step)

m < n ⊦ n0 ∈ ns -- m ∧ n0 < n ↔ n0 ≠ m ∧ n0 ∈ below(ns, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
m < n ⊦ n0 ∈ ns ∧ n0 < n ↔ n0 ∈ below(ns, n), n0 = m

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ ns -- n0 ↔ n ≠ n0 ∧ n ∈ ns; (s)