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Proof step 5 from proof reach-n-path-n (previous step)

⊦ reachable-1(H, r, r0) ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0
Proof step 7:
⊦ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r].nxt = r0 ↔ (∃ x. path(x, H) ∧ hd x = r ∧ x.last = r0 ∧ # x = 2)

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] → [r0, r, H] flags: rewrite, current

Additional information

Used terms: r0, r, H