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Proof step 62 from proof acyclic-rem-not-reachable (previous step)

x0 = [], ce.nxt = H[H[r0].nxt].nxt, r1 ' + x = x0 + r0 ', r0 ∈ H, path(r ' + x1 + H[r0].nxt ', H), path(r ' + (x1 + H[r0].nxt ' + x0) + r0 ', H), H[r0].nxt ∈ H, r1 ∈ x0 ∨ r1 = r0, ∀ r1. ¬ reachable(H[r1].nxt, r1, H), r0 = r1 ∨ r0 ∈ x ⊦ H[r0].nxt = null, r = H[r0].nxt, r0 = r, r0 = H[r0].nxt, r0 ∈ x1, r ∈ x1, H[r0].nxt ∈ x1, r ∈ x0, r0 ∈ x0, H[r0].nxt ∈ x0, dups(x1 + x0), dups(x1), dups(x0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 63:
ce.nxt = H[H[r0].nxt].nxt, path(r ' + x1 + H[r0].nxt ' + r0 ', H), path(r ' + x1 + H[r0].nxt ', H), r0 ∈ H, H[r0].nxt ∈ H, ∀ r1. ¬ reachable(H[r1].nxt, r1, H) ⊦ r0 = H[r0].nxt, r0 = r, r = H[r0].nxt, H[r0].nxt = null, H[r0].nxt ∈ x1, r ∈ x1, r0 ∈ x1, dups(x1)

Rule argument

Additional information

Used simplifier rules: e-01: ⊦ ¬ dups([]); from specification list-dup[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]%in-empty: ⊦ ¬ r ∈ []; from specification list[reflist]%c-03: ⊦ r ' = r0 ' + x0 ↔ r = r0 ∧ x0 = []; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]