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Proof step 7 from proof fromnext-reachable (previous step)

path(r ' + x, H), x.last ∈ H ⊦ x = [], r = x.last, reachable(H[r].nxt, x.last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 9:
path(r ' + x, H), x.last ∈ H ⊦ x = [], r = x.last, ∃ x0. path(H[r].nxt ' + x0, H) ∧ (H[r].nxt ' + x0).last = x.last

Rule argument

spec: inst: name: reachable-def seq: ⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) subst: [H, r0, r] → [H, x.last, H[r].nxt] flags: rewrite, current

Additional information

Used terms: H, x.last, H[r].nxt