[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 21 from proof cyclic-weak-def (previous step)

# x1 = 1 + # H, path(r ' + x1, H), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

User applied rule insert lemma

And obtained the following new goals

Proof step 17:
⊦ path(x, H) ∧ dups(x) → cyclic(hd x, H)
Proof step 20:
path(r ' + x1, H) ∧ dups(r ' + x1) → cyclic(hd (r ' + x1), H), # x1 = 1 + # H, path(r ' + x1, H), ∀ n. ∃ r0. reachable-n(H, n, r, r0) ⊦ cyclic(r, H)

Rule argument

[x0lemmaarg: spec-name: instance-name: lemma-name: path-dups antecedent: succedent: path(x, H) ∧ dups(x) → cyclic(hd x, H) substlist: [x, H] → [r ' + x1, H] add preconditions?: F is rewrite lemma?: F current spec?: T rotate lemma?: F replace all?: F paths: () dummy: () ]

Additional information

[[CONCRETESIMPRULES : ()], [EXTRATERMS : (r ' + x1, H)]]