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Proof step 5 from proof reachset-del (previous step)

∀ b. b ∈ S → reach(a, b, n) ∧ ¬ reach<(a, b, n) ⊦ reachS(a, S -- b, n)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ reachS(a, S, n) ↔ (∀ b. b ∈ S → reach(a, b, n) ∧ ¬ reach<(a, b, n))
Proof step 4:
∀ b. b ∈ S → reach(a, b, n) ∧ ¬ reach<(a, b, n) ⊦ ∀ b0. b0 ∈ S -- b → reach(a, b0, n) ∧ ¬ reach<(a, b0, n)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: reachset-def antecedent: succedent: reachS(a, S, n) ↔ (∀ b. b ∈ S → reach(a, b, n) ∧ ¬ reach<(a, b, n)) substlist: [n, S, a] → [n, S -- b, a] add preconditions?: F is rewrite lemma?: T current spec?: T rotate lemma?: F replace all?: T paths: ((1, 0, 0)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (n, S -- b, a)]]