Nuprl Lemma : LTL-identities
∀es:EO. ∀[P:E ─→ ℙ]. ([][]P ≡ []P ∧ <><>P ≡ <>P ∧ <>P ≡ (TR ∪ P) ∧ []¬¬P ≡ ¬<>¬P ∧ ¬¬<>P ≡ ¬[]¬P)
Proof
Definitions occuring in Statement :
es-TR: TR,
es-equiv: P ≡ Q,
es-not: ¬P,
es-until: (P ∪ Q),
es-diamond: <>P,
es-box: []P,
es-E: E,
event_ordering: EO,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
and: P ∧ Q,
function: x:A ─→ B[x]
Lemmas :
es-le_wf,
es-E_wf,
all_wf,
es-le_transitivity,
exists_wf,
es-le_weakening_eq,
es-locl_wf,
true_wf,
not_wf,
event_ordering_wf,
es-le-self
\mforall{}es:EO. \mforall{}[P:E {}\mrightarrow{} \mBbbP{}]. ([][]P \mequiv{} []P \mwedge{} <><>P \mequiv{} <>P \mwedge{} <>P \mequiv{} (TR \mcup{} P) \mwedge{} []\mneg{}\mneg{}P \mequiv{} \mneg{}<>\mneg{}P \mwedge{} \mneg{}\mneg{}<>P \mequiv{} \mneg{}[]\mneg{}P)
Date html generated:
2015_07_17-AM-08_49_46
Last ObjectModification:
2015_01_27-PM-02_29_05
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