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]
Definitions unfolded in proof :
es-not: ¬P,
es-box: []P,
es-diamond: <>P,
es-equiv: P ≡ Q,
es-TR: TR,
es-until: (P ⋃ Q),
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
rev_implies: P ⇐ Q,
guard: {T},
exists: ∃x:A. B[x],
uimplies: b supposing a,
true: True,
not: ¬A,
false: False
Latex:
\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:
2016_05_16-AM-09_48_38
Last ObjectModification:
2015_12_28-PM-09_41_29
Theory : new!event-ordering
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