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Proof step 91 from proof rem-stays-reachable-aux2 (previous step)

H[x0.last].nxt = H[r2].nxt, (x0.last ' + x1).last = x0.last, x1 + r2 ' = H[r2].nxt ' + r0 ' + y, path(x0.last ' + x1, H), x0.last ∈ H, path(x0.last ' + x1 + r2 ', H), H[r2].nxt ∈ H, r2 ∈ H, path(r2 ' + x0, H), r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y, H[r2].nxt ∈ x1 ∨ H[r2].nxt = r2 ⊦ x0.last = null, x0.last = r2, H[r2].nxt = null, x0 = [], dups(x1), r2 ∈ x0, dups(x0), x0.last ∈ x1, r2 ∈ x1

User applied rule insert elim lemma

And obtained the following new goals

Proof step 92:
x0 = x + r ', H[r].nxt = H[r2].nxt, (r ' + x1).last = r, x1 + r2 ' = H[r2].nxt ' + r0 ' + y, path(r ' + x1, H), r ∈ H, path(r ' + x1 + r2 ', H), H[r2].nxt ∈ H, r2 ∈ H, path(r2 ' + x0, H), r2 = H[r2].nxt ∨ r2 = r0 ∨ r2 ∈ y, H[r2].nxt ∈ x1 ∨ H[r2].nxt = r2 ⊦ r = null, r = r2, H[r2].nxt = null, x0 = [], dups(x1), r2 ∈ x0, dups(x0), r ∈ x1, r2 ∈ x1

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, r, x] flags: []

Additional information

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