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Proof step 66 from proof add-preserves-reachable-rev (previous step)

H[r1].nxt = H[ce.nxt].nxt, path(H[r].nxt ' + x0, H[r1, ce]), reachable(H[r].nxt, ce.nxt, H), reachable(r, r1, H), r ∈ H, ce.nxt ∈ H, r1 ∈ H, x0.last ∈ H[r1, ce] ⊦ x0.last = ce.nxt, ce.nxt = null, r = r1, r = null, x0 = [], reachable(r, ce.nxt, H), reachable(r, x0.last, H)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 67:
⊦ reachable(H[r].nxt, r0, H) ∧ r ≠ r0 ∧ r ≠ null ∧ r ∈ H → (reachable(r, r0, H) ↔ true)

Rule argument

spec: <toplevel> name: fromnext-reachable-rev seq: ⊦ reachable(H[r].nxt, r0, H) ∧ r ≠ r0 ∧ r ≠ null ∧ r ∈ H → (reachable(r, r0, H) ↔ true) subst: [H, r0, r] → [H, ce.nxt, r] flags: <all paths>

Additional information

Used simplifier rules: self-reachable: ⊦ reachable(r, r, H) ↔ r ≠ null ∧ r ∈ H;%reachable-notnullinH: ⊦ reachable(r, r1, H) → (r1 ∈ H ↔ true); Used terms: H, ce.nxt, r