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Proof step 8 from proof ex1-shiftw-inst (previous step)

((_∃ rP -* P))(H1), P0(H0), H1 ⊥ H0 ⊦ (((rP(r) -* P) * P0))(H1 ∪ H0), ((rP(r) -* P))(H1)

User applied rule insert rewrite lemma

And obtained the following new goals

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

Rule argument

spec: <toplevel> name: ex1-shiftw seq: ⊦ ((_∃ rP -* P))(H) ↔ (∀ r. ((rP(r) -* P))(H)) subst: [H, P, rP] → [H1, P, rP] flags: <all paths>

Additional information

Used terms: H1, P, rP