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

n ≤ m ⊦ n0 ∈ below(ns -- m, n) ↔ n0 ∈ below(ns, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ n ∈ below(ns, m) ↔ n ∈ ns ∧ n < m
Proof step 6:
n ≤ m ⊦ n0 ∈ ns -- m ∧ n0 < n ↔ n0 ∈ below(ns, n)

Rule argument

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

Additional information

Used terms: n, ns -- m, n0