[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 11 from proof legal-noncylic-equiv-reaches-null (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 5:
⊦ reachable(r, r0, H) ↔ r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0)
Proof step 10:
H[r0] .nxt = null, legal(H), r ∈ H, reachable-n(H, n0, r, r0) ⊦ r = null, r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0), ∃ r0. reachable(r, r0, H) ∧ H[r0] .nxt = null

Rule argument

[x0lemmaarg: spec-name: path-reachable instance-name: lemma-name: k-reachable-def antecedent: succedent: reachable(r, r0, H) ↔ r ≠ null ∧ r ∈ H ∧ reachable*(H, r, r0) substlist: [H, r0, r] → [H, r0, r] 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, r)]]