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Proof step 9 from proof modified-stays-reachable (previous step)

path(r ' + x, H) ⊦ ∃ x0. path(r ' + x0, H[(r ' + x0).last, ce]) ∧ (r ' + x0).last = (r ' + x).last

User applied rule structural induction

And obtained the following new goals

Proof step 10:
path(r ' + [], H) ⊦ ∃ x0. path(r ' + x0, H[(r ' + x0).last, ce]) ∧ (r ' + x0).last = (r ' + []).last
Proof step 12:
path(r ' + (r0 + x0), H), ∀ r, H, ce. path(r ' + x0, H) → (∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + x0).last) ⊦ ∃ x1. path(r ' + x1, H[(r ' + x1).last, ce]) ∧ (r ' + x1).last = (r ' + (r0 + x0)).last

Rule argument

indvar: x

Additional information

Used simplifier rules: reflist freely generated by [], +;;