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Proof step 93 from proof rem-stays-reachable-aux2 (previous step)

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 ' + x + r ', 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, r ∈ x1, r2 ∈ x1, dups(x1), r2 ∈ x, r ∈ x, dups(x)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-last inst: reflist name: lapp seq: ⊦ x0 ≠ [] → (x1 + x0).last = x0.last subst: [x0, x1] → [x1, r '] flags: rewrite

Additional information

Used simplifier rules: lin-01: ⊦ x0.last ∈ x0 ↔ x0 ≠ []; from specification list-last[reflist]%app: ⊦ x0 + [] = x0; from specification list[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%l: ⊦ r '.last = r; from specification list-last[reflist]%Nil: ⊦ [] + x0 = x0; from specification list[reflist]%c-03: ⊦ r ' = r0 ' + x0 ↔ r = r0 ∧ x0 = []; from specification list[reflist]%e-01: ⊦ r ' + x0 ≠ []; from specification list[reflist] Used terms: x1, r '