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Proof step 5 from proof ls-add-1 (previous step)

∀ n0. n0 = n ∨ n0 ∈ ns → ¬ n < n0 ⊦ ns < n + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n)
Proof step 7:
∀ n0. n0 = n ∨ n0 ∈ ns → ¬ n < n0 ⊦ ∀ n0. n0 ∈ ns → n0 < n + 1

Rule argument

spec: oset, inst: nat-set name: Greater seq: ⊦ ns < n ↔ (∀ n0. n0 ∈ ns → n0 < n) subst: [n, ns] → [n + 1, ns] flags: <all paths>

Additional information

Used terms: n + 1, ns