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Proof step 10 from proof reachable-split-last (previous step)

path(r ' + x, H), x.last ∈ H ⊦ r = x.last, x = [], ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = x.last ∧ H[r1].nxt ≠ null

User applied rule insert elim lemma

And obtained the following new goals

Proof step 11:
x = x1 + r0 ', path(r ' + x, H), r0 ∈ H ⊦ r = r0, x = [], ∃ r1. reachable(r, r1, H) ∧ H[r1].nxt = r0 ∧ H[r1].nxt ≠ null

Rule argument

spec: list-last inst: reflist name: last-elim seq: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r ' subst: [x0, r, x1] → [x, r0, x0] flags: []

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x, r0, x0