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Proof step 5 from proof reach-n-next-legal (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0))

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: reachable-n-rec-rev antecedent: succedent: reachable-n(H, n + 1, r, r0) ↔ (∃ r1. reachable-n(H, n, r, r1) ∧ reachable-1(H, r1, r0)) substlist: [r0, r, n, H] → [r0, r, m, H] add preconditions?: F is rewrite lemma?: T current spec?: F rotate lemma?: F replace all?: T paths: ((0, 0, 2)) dummy: () ]

Additional information

[[CONCRETESIMPRULES : ([CSIMPSEQ : ⊦ reachable-1(H, r, r0) ↔ r ≠ null ∧ r0 ≠ null ∧ r ∈ H ∧ r0 ∈ H ∧ H[r] .nxt = r0])], [EXTRATERMS : (r0, r, m, H)]]