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Proof step 10 from proof modnotreachable-reachable-rev-weak (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
path(H[r].nxt ' + x0, H[r0, ce]), r0 ∈ H, r ∈ H, ∀ r, H, r0, ce. path(r ' + x0, H[r0, ce]) ∧ r0 ∈ H → r0 = null ∨ reachable(r, r0, H) ∨ reachable(r, (r ' + x0).last, H) ⊦ r = r0, r = null, r0 = null, reachable(r, (H[r].nxt ' + x0).last, H), reachable(r, r0, H)

Rule argument

Additional information

Used simplifier rules: ⊦ r ∈ H[r0, ce] ↔ r = r0 ∨ r ∈ H; (ws)