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Proof step 2 from proof below-rem-in (previous step)

m < n ⊦ below(ns -- m, n) = below(ns, n) -- m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0)
Proof step 4:
m < n ⊦ ∀ n0. n0 ∈ below(ns -- m, n) ↔ n0 ∈ below(ns, n) -- m

Rule argument

spec: set-basic, inst: nat-set name: Extension seq: ⊦ ns = ns0 ↔ (∀ n. n ∈ ns ↔ n ∈ ns0) subst: [ns0, ns] → [below(ns, n) -- m, below(ns -- m, n)] flags: <all paths>

Additional information

Used terms: below(ns, n) -- m, below(ns -- m, n)