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Proof step 8 from proof reachable-addnew (previous step)

path(r ' + x, H) ⊦ x = [], reachable(r, x.last, H[r2, ce]), r2 ∈ H

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 9:
⊦ reachable(r, r0, H) ↔ (∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0)
Proof step 10:
path(r ' + x, H) ⊦ x = [], r2 ∈ H, ∃ x0. path(r ' + x0, H[r2, ce]) ∧ (r ' + x0).last = x.last

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[r2, ce], x.last, r] flags: <all paths>

Additional information

Used terms: H[r2, ce], x.last, r