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Proof step 7 from proof modnotreachable-reachable-rev (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
path(H[r0, ce][r].nxt ' + x0, H[r0, ce]), r ∈ H[r0, ce], (H[r0, ce][r].nxt ' + x0).last ∈ H[r0, ce], r0 ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0[r3, ce0]) ∧ r3 ∈ H0 → reachable(r2, r3, H0) ∨ reachable(r2, (r2 ' + x0).last, 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 ↔ true);% ⊦ (r ' + r0 ' + x0).last = (r0 ' + x0).last; (s)%a: ⊦ (x0 + x1) + x2 = x0 + x1 + x2; from specification list[reflist]% ⊦ r + x0 = r ' + x0; (s)