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Proof step 33 from proof rem-preserves-monls (previous step)

mon<(⌜nnf⌝ ) ⊦ mon<(lim(λ n. rem(⌜nnf to n⌝ , np)))

User applied rule insert lemma

And obtained the following new goals

Proof step 34:
⊦ (∀ n. mon<(nσf(n))) ∧ mon(nσf) → (mon<(lim(λ n. nσf(n))) ↔ true)
Proof step 35:
mon<(⌜nnf⌝ ), (∀ n. mon<(rem(⌜nnf to n⌝ , np))) ∧ mon(λ n. rem(⌜nnf to n⌝ , np)) → (mon<(lim(λ n. rem(⌜nnf to n⌝ , np))) ↔ true) ⊦ mon<(lim(λ n. rem(⌜nnf to n⌝ , np)))

Rule argument

spec: <toplevel> name: monls-mon-implies-monls seq: ⊦ (∀ n. mon<(nσf(n))) ∧ mon(nσf) → (mon<(lim(λ n. nσf(n))) ↔ true) subst: [nσf] → [λ n. rem(⌜nnf to n⌝ , np)]

Additional information

Used terms: λ n. rem(⌜nnf to n⌝ , np)