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

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

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: in-below seq: ⊦ n ∈ below(ns, m) ↔ n ∈ ns ∧ n < m subst: [m, ns, n] → [n, ns, n0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m ≤ n → (n < m ↔ false); (s) Used terms: n, ns, n0