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Proof step 31 from proof rem-stays-reachable-aux (previous step)

x0.last = H[r0].nxt, ce.nxt = H[x0.last].nxt, path(r ' + x0, H[r0, ce]), path(r ' + x1 + r0 ', H), x0.last ∈ H, r0 ∈ H, x0.last ∈ H[r0, ce] ⊦ x0.last = ce.nxt, x0.last = null, r = r0, r = x0.last, x0 = [], dups(x0), dups(x1), r ∈ x1, r ∈ x0, r0 ∈ x1, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0, ∃ x. path(r ' + x + x0.last ', H) ∧ ¬ r0 ∈ x

User applied rule insert elim lemma

And obtained the following new goals

Proof step 32:
ce.nxt = H[r1].nxt, r1 = H[r0].nxt, x0 = x2 + r1 ', path(r ' + x1 + r0 ', H), path(r ' + x0, H[r0, ce]), r1 ∈ H[r0, ce], r0 ∈ H, r1 ∈ H ⊦ r = r1, r = r0, r1 = null, r1 = ce.nxt, x0 = [], dups(x1), dups(x0), r0 ∈ x1, r ∈ x0, r ∈ x1, ∃ x. path(r ' + x + r1 ', H) ∧ ¬ r0 ∈ x, ∃ x0. path(H[r0].nxt ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

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] → [x0, r1, x2]

Additional information

Used simplifier rules: x0 ≠ [] ⊦ r = x0.last ∧ x1 = x0.butlast ↔ x0 = x1 + r '; (elim) Used terms: x0, r1, x2