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Proof step 15 from proof modnotreachable-reachable-rev-weak (previous step)

(H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, r ∈ H, path(H[r].nxt ' + x0, H[r0, ce]), r0 ∈ H, path(H[r].nxt ' + x, H) ⊦ r = r0, r0 = null, r = null, reachable(r, r0, H), reachable(r, (H[r].nxt ' + x0).last, H), reachable(H[r].nxt, r0, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 17:
(H[r].nxt ' + x).last = (H[r].nxt ' + x0).last, r ∈ H, path(H[r].nxt ' + x0, H[r0, ce]), r0 ∈ H, path(H[r].nxt ' + x, H) ⊦ r = r0, r0 = null, r = null, reachable(r, r0, H), ∃ x. path(r ' + x, H) ∧ (r ' + x).last = (H[r].nxt ' + x0).last, reachable(H[r].nxt, r0, H)

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, (H[r].nxt ' + x0).last, r] flags: rewrite, current

Additional information

Used terms: H, (H[r].nxt ' + x0).last, r