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Proof step 14 from proof reachable-modbehind (previous step)

r = r1, path(H[r].nxt ' + x0, H), reachable((H[r].nxt ' + x0).last, r1, H), r ∈ H[r1, ce], (H[r].nxt ' + x0).last ∈ H, r1 ∈ H, r ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) ∧ reachable((r2 ' + x0).last, r3, H0) → path(r2 ' + x0, H0[r3, ce0]) ∨ reachable(r3, (r2 ' + x0).last, H0) ⊦ r = null, reachable(r1, (H[r].nxt ' + x0).last, H), path(H[r1, ce][r].nxt ' + x0, H[r1, ce]) ∧ H[r1, ce][r].nxt = H[r].nxt

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
path(H[r1].nxt ' + x0, H), reachable((H[r1].nxt ' + x0).last, r1, H), r1 ∈ H, (H[r1].nxt ' + x0).last ∈ H, ∀ r2, H0, r3, ce0. path(r2 ' + x0, H0) ∧ reachable((r2 ' + x0).last, r3, H0) → path(r2 ' + x0, H0[r3, ce0]) ∨ reachable(r3, (r2 ' + x0).last, H0) ⊦ r1 = null, reachable(r1, (H[r1].nxt ' + x0).last, H), path(ce.nxt ' + x0, H[r1, ce]) ∧ ce.nxt = H[r1].nxt

Rule argument

Additional information

Used simplifier rules: ⊦ H[r, ce][r] = ce; (s)% ⊦ r ∈ H[r, ce]; (s)