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Proof step 33 from proof cont-monotone (previous step)

S0(x0), f(S0)(x), S0 ⊆ S, f(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0))(x) ⊦ S(x0), f(S)(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x))
Proof step 35:
S0(x0), f(S0)(x), ∀ x. S0(x) → S(x), f(λ x0. ∃ n. (n = 0 ⊃ S0;S)(x0))(x) ⊦ S(x0), f(S)(x)

Rule argument

spec: monotone-set-fixpoint inst: name: subseteq-def seq: ⊦ S ⊆ S0 ↔ (∀ x. S(x) → S0(x)) subst: [S0, S] → [S, S0] flags: rewrite

Additional information

Used terms: S, S0