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Proof step 16 from proof frommodified (previous step)

reachable(ce.nxt, r0, H[r, ce]), ce.nxt ∈ H, r0 ∈ H ⊦ ce.nxt = null, r = r0, r = null, reachable(r, r0, H[r, ce])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 17:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 18:
∃ x. path(ce.nxt ' + x, H[r, ce]) ∧ (ce.nxt ' + x).last = r0, ce.nxt ∈ H, r0 ∈ H ⊦ ce.nxt = null, r = r0, r = null, reachable(r, r0, H[r, ce])

Rule argument

spec: inst: name: reachable-def seq: ⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0) subst: [H, r0, r] → [H[r, ce], r0, ce.nxt] flags: rewrite, current

Additional information

Used terms: H[r, ce], r0, ce.nxt