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Proof step 25 from proof frommodified (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 27:
path(ce.nxt ' + x, H[r, ce]), ce.nxt ∈ H, x.last ∈ H ⊦ r = null, x = [], ce.nxt = null, r = x.last, ∃ x0. path(r ' + x0, H[r, ce]) ∧ (r ' + x0).last = x.last

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], x.last, r] flags: rewrite, current

Additional information

Used terms: H[r, ce], x.last, r