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Proof step 25 from proof k-reachable-def (previous step)

reachable-n(H, n, H[r].nxt, x0.last), path(H[r].nxt ' + x0, H), r ∈ H ⊦ x0 = [], r = null, reachable-1(H, r, H[r].nxt)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0

Rule argument

spec: inst: name: reachable-1-def seq: ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0 subst: [r0, r, H] → [H[r].nxt, r, H] flags: rewrite, current

Additional information

Used simplifier rules: path-first-in-H: ⊦ path(r ' + x, H) → (¬ r ∈ H ↔ false);%null-not-start-of-path: ⊦ ¬ path(null ' + x, H);%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist] Used terms: H[r].nxt, r, H