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Proof step 4 from proof below-rem-in (previous step)

m < n ⊦ ∀ n0. n0 ∈ below(ns -- m, n) ↔ n0 ∈ below(ns, n) -- m

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m < n ⊦ n0 ∈ below(ns -- m, n) ↔ n0 ≠ m ∧ n0 ∈ below(ns, n)

Rule argument

Additional information

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