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Proof step 6 from proof reach-reachnext (previous step)

path(r ' + x, H), (r ' + x).last ∈ H ⊦ reachable(r, H[(r ' + x).last].nxt, H) ↔ H[(r ' + x).last].nxt ≠ null ∧ H[(r ' + x).last].nxt ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 8:
path(r ' + x, H), (r ' + x).last ∈ H ⊦ (∃ x0. path(r ' + x0, H) ∧ (r ' + x0).last = H[(r ' + x).last].nxt) ↔ H[(r ' + x).last].nxt ≠ null ∧ H[(r ' + x).last].nxt ∈ H

Rule argument

spec: <toplevel> name: reachable-def seq: ⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) subst: [H, r0, r] → [H, H[(r ' + x).last].nxt, r] flags: <all paths>

Additional information

Used terms: H, H[(r ' + x).last].nxt, r