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Proof step 36 from proof k-reachable-def (previous step)

n0 = 0, H[r].nxt ∈ H, r ∈ H, reachable-n(H, n0, H[r].nxt, r0), n0 = 0 ∨ path(H[r].nxt ' + x, H) ∧ (H[r].nxt ' + x).last = r0 ⊦ H[r].nxt = null, r = null, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = r0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 37:
r ∈ H, H[r].nxt ∈ H ⊦ r = null, H[r].nxt = null, ∃ x. path(r ' + x, H) ∧ (r ' + x).last = H[r].nxt

Rule argument

Additional information

Used simplifier rules: reachable-n-base: ⊦ reachable-n(H, 0, r, r0) ↔ r = r0;