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Proof step 22 from proof legal-noncylic-equiv-reaches-null (previous step)

legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H ∧ H[r0] .nxt ∈ H ∧ H[r0] .nxt = H[r0] .nxt, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 4:
⊦ legal(H) ∧ r ∈ H ∧ H[r] .nxt ≠ null → (¬ H[r] .nxt ∈ H ↔ false)
Proof step 21:
legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H

Rule argument

[emptyarg]

Additional information

[[CONCRETESIMPRULES : ()]]