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Proof step 3 from proof k-reachable-def (previous step)

⊦ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) ↔ r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ reachable*(H, r, r0) ↔ (∃ n. reachable-n(H, n, r, r0))
Proof step 5:
⊦ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) ↔ r ≠ null ∧ r ∈ H ∧ (∃ n. reachable-n(H, n, r, r0))

Rule argument

spec: inst: name: reachable-star-def seq: ⊦ reachable*(H, r, r0) ↔ (∃ n. reachable-n(H, n, r, r0)) subst: [r0, r, H] → [r0, r, H] flags: rewrite, current

Additional information

Used terms: r0, r, H