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Proof step 57 from proof rem-stays-reachable-aux2 (previous step)

r0 = H[r0].nxt, (r0 ' + x0).last = x1.last, x1.last ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + (x2 + x1.last ') + r0 ', H), path(r ' + x1, H) ⊦ r0 = r, r0 = null, r = x1.last, r0 = x1.last, x1 = [], x1.last ∈ x2, dups(x2), r ∈ x2, dups(x1), r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x2

User applied rule insert elim lemma

And obtained the following new goals

Proof step 58:
x1 = x + r1 ', r0 = H[r0].nxt, (r0 ' + x0).last = r1, r1 ∈ H, path(r0 ' + x0, H), r0 ∈ H, path(r ' + (x2 + r1 ') + r0 ', H), path(r ' + x1, H) ⊦ r0 = r, r0 = null, r = r1, r0 = r1, x1 = [], r1 ∈ x2, dups(x2), r ∈ x2, dups(x1), r ∈ x1, dups(x0), r0 ∈ x0, r0 ∈ x2

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] → [x1, r1, x] flags: []

Additional information

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