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Proof step 10 from proof reachable-trans (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ 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, r1, 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, r1, r