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Proof step 6 from proof modnotreachable-reachable-rev (previous step)

∀ r0, H, r, ce. r0 ∈ H ∧ path(r ' + x0, H[r0, ce]) ∧ (r ' + x0).last ∈ H[r0, ce] → reachable(r, (r ' + x0).last, H) ∨ reachable(r, r0, H), r0 ∈ H, path(r ' + (r1 + x0), H[r0, ce]), (r ' + (r1 + x0)).last ∈ H[r0, ce] ⊦ reachable(r, (r ' + (r1 + x0)).last, H), reachable(r, r0, H)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 7:
(H[r0, ce][r].nxt ' + x0).last ∈ H[r0, ce], path(H[r0, ce][r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], r0 ∈ H, ∀ r2, H0, r3, ce0. r2 ∈ H0 ∧ path(r3 ' + x0, H0[r2, ce0]) → reachable(r3, (r3 ' + x0).last, H0) ∨ reachable(r3, r2, H0) ⊦ r = null, reachable(r, (H[r0, ce][r].nxt ' + x0).last, H), reachable(r, r0, H)

Rule argument

Additional information

Used simplifier rules: path-cons: ⊦ path(r ' + r0 ' + x, H) ↔ ¬ ¬(r ∈ H ∧ r ≠ null ∧ H[r].nxt = r0 ∧ path(r0 ' + x, H));%path-last: ⊦ path(r ' + x, H) → (¬ (r ' + x).last ∈ H ↔ false);%l-05: ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; from specification list-last[reflist]%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]%c: ⊦ r + x0 = r ' + x0; from specification list[reflist]