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Proof step 9 from proof reach-n-next-legal (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 2:
⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r] .nxt = r0
Proof step 8:
r ∈ H, legal(H), reachable-n(H, n, r, r0) ⊦ H[r0] .nxt = null, r = null, r0 ≠ null ∧ H[r0] .nxt ≠ null ∧ r0 ∈ H ∧ H[r0] .nxt ∈ H ∧ H[r0] .nxt = H[r0] .nxt

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, 2)) dummy: () ]

Additional information

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