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Proof step 23 from proof legal-noncylic-equiv-reaches-null (previous step)

legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, reachable-1(H, r0, H[r0] .nxt), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 3:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r] .nxt = r0
Proof step 22:
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

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-1-def antecedent: succedent: reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r] .nxt = r0 substlist: [r0, r, H] → [H[r0] .nxt, r0, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((1, 0, 1)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (H[r0] .nxt, r0, H)]]