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Proof step 4 from proof fixpoint-nu (previous step)

monotone(f) ⊦ f(ν(f))(x) ↔ ¬ μ(compl(f))(x)

User applied rule insert lemma

And obtained the following new goals

Proof step 5:
monotone(f) ⊦ f(μ(f)) = μ(f)
Proof step 6:
compl(f)(μ(compl(f))) = μ(compl(f)), monotone(f) ⊦ f(ν(f))(x) ↔ ¬ μ(compl(f))(x)

Rule argument

spec: inst: name: fixpoint seq: monotone(f) ⊦ f(μ(f)) = μ(f) subst: [f] → [compl(f)] flags: current, []

Additional information

Used simplifier rules: compl-monotone: ⊦ monotone(f) → (¬ monotone(compl(f)) ↔ false); Used terms: compl(f)