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Proof step 5 from proof le-add-bound (previous step)

n ≤ m, ∀ n0. n0 ∈ ns → n0 < n ⊦ ns < m

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:
n ≤ m, ∀ n0. n0 ∈ ns → n0 < n ⊦ ∀ n0. n0 ∈ ns → n0 < m

Rule argument

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

Additional information

Used terms: m, ns