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Proof step 52 from proof reachable-addnew-rev (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 53:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 54:
(ce.nxt ' + x).last ∈ H, r ∈ H, path(ce.nxt ' + x, H[H[r].nxt, ce]) ⊦ H[r].nxt = ce.nxt, r = ce.nxt, r = null, r = H[r].nxt, H[r].nxt = null, reachable(r, (ce.nxt ' + x).last, H), dups(x), ce.nxt ∈ x, H[r].nxt ∈ x, r ∈ x, H[r].nxt ∈ H, ∃ x0. path(ce.nxt ' + x0, H) ∧ (ce.nxt ' + x0).last = (ce.nxt ' + 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, (ce.nxt ' + x).last, ce.nxt] flags: rewrite, current

Additional information

Used terms: H, (ce.nxt ' + x).last, ce.nxt