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Proof step 10 from proof rem-stays-reachable-aux1 (previous step)

x.last = H[r0].nxt, path(H[x.last].nxt ' + x, H), r0 ∈ H, x.last ∈ H ⊦ x.last = H[x.last].nxt, x.last = null, x = [], reachable(H[x.last].nxt, r0, H), H[x.last].nxt ∈ x, dups(x), ∃ x. path(H[r0].nxt ' + x + H[r0].nxt ', H) ∧ ¬ r0 ∈ x

User applied rule insert elim lemma

And obtained the following new goals

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

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, r, x0] flags: []

Additional information

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