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Proof step 5 from proof rem-stays-reachable-aux2 (previous step)

H[r0].nxt = H[r1].nxt, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r1, reachable(r, r0, H), H[r1].nxt ∈ H, r1 ∈ H, r0 ∈ H ⊦ H[r1].nxt = null, reachable(r0, r1, H), ∃ x. path(r ' + x + H[r1].nxt ', H) ∧ ¬ r0 ∈ x

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
H[r0].nxt = H[(r ' + x).last].nxt, path(r ' + x, H), reachable(r, r0, H), H[r0].nxt ∈ H, (r ' + x).last ∈ H, r0 ∈ H ⊦ H[r0].nxt = null, reachable(r0, (r ' + x).last, H), ∃ x0. path(r ' + x0 + H[r0].nxt ', H) ∧ ¬ r0 ∈ x0

Proof step 5 from proof rem-stays-reachable-aux2 (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Rule argument

Additional information