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Proof step 8 from proof ex3-shiftw-inst (previous step)

((_∃ oP -* P))(H1), P0(H0), H1 ⊥ H0 ⊦ (((oP(o) -* P) * P0))(H1 ∪ H0), ((oP(o) -* P))(H1)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ ((_∃ oP -* P))(H) ↔ (∀ o. ((oP(o) -* P))(H))
Proof step 10:
P0(H0), H1 ⊥ H0, ∀ o. ((oP(o) -* P))(H1) ⊦ (((oP(o) -* P) * P0))(H1 ∪ H0), ((oP(o) -* P))(H1)

Rule argument

spec: <toplevel> name: ex3-shiftw seq: ⊦ ((_∃ oP -* P))(H) ↔ (∀ o. ((oP(o) -* P))(H)) subst: [H, P, oP] → [H1, P, oP] flags: <all paths>

Additional information

Used terms: H1, P, oP