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

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

Rule argument

Additional information

Used simplifier rules: ⊦ r ≠ r0 → (r ∈ H[r0, ce] ↔ r ∈ H); (s)