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Proof step 6 from proof inos-greater-rem (previous step)

∀ n. inodekey(n) ∈ ri → n < maxino ⊦ (ri \ ks).inos < maxino

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n)
Proof step 8:
∀ n. inodekey(n) ∈ ri → n < maxino ⊦ ∀ n0. n0 ∈ (ri \ ks).inos → n0 < maxino

Rule argument

spec: oset, inst: nat-set name: Greater seq: ⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n) subst: [n, ns] → [maxino, (ri \ ks).inos] flags: <all paths>

Additional information

Used terms: maxino, (ri \ ks).inos