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Proof step 12 from proof reach-n-path-n (previous step)

# x = 2, path(x, H) ⊦ hd x ≠ null ∧ H[hd x].nxt ≠ null ∧ hd x ∈ H ∧ H[hd x].nxt ∈ H ∧ H[hd x].nxt = x.last

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 13:
x = r + x1 ∧ x ≠ [], # x = 2, path(x, H) ⊦ r ≠ null ∧ H[r].nxt ≠ null ∧ r ∈ H ∧ H[r].nxt ∈ H ∧ H[r].nxt = x.last

Rule argument

spec: list-data inst: reflist name: elim-list-c seq: x0 ≠ [] ⊦ r = hd x0 ∧ x1 = tl x0 ↔ x0 = r + x1 subst: [x0, r, x1] → [x, r, x0] flags:

Additional information

Used simplifier rules: size-01: ⊦ # [] = 0; from specification list-data[reflist]%x0 ≠ [] ⊦ r = hd x0 ∧ x1 = tl x0 ↔ x0 = r + x1; (elim) Used terms: x, r, x0