Nuprl Lemma : cond_equiv_to_causl
∀es:EO
∀[R:E ─→ E ─→ ℙ]. ∀[P:E ─→ ℙ].
(R => λe,e'. (e < e')
⇒ (∀x,y:E. (((P x) ∧ (P y)) ⇒ (((R x y) ∨ (x = y ∈ E)) ∨ (R y x))))
⇒ (∀x,y:E. (((P x) ∧ (P y)) ⇒ (R x y ⇐⇒ (x < y)))))
Proof
Definitions occuring in Statement :
es-causl: (e < e'),
es-E: E,
event_ordering: EO,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
or: P ∨ Q,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
all_wf,
or_wf,
equal_wf,
rel_implies_wf,
es-E_wf,
es-causl_wf,
event_ordering_wf,
cond_rel_equivalent,
es-causl_transitivity2,
es-causle_weakening,
es-causl_irreflexivity
\mforall{}es:EO
\mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[P:E {}\mrightarrow{} \mBbbP{}].
(R => \mlambda{}e,e'. (e < e')
{}\mRightarrow{} (\mforall{}x,y:E. (((P x) \mwedge{} (P y)) {}\mRightarrow{} (((R x y) \mvee{} (x = y)) \mvee{} (R y x))))
{}\mRightarrow{} (\mforall{}x,y:E. (((P x) \mwedge{} (P y)) {}\mRightarrow{} (R x y \mLeftarrow{}{}\mRightarrow{} (x < y)))))
Date html generated:
2015_07_17-AM-09_09_26
Last ObjectModification:
2015_01_27-PM-00_47_05
Home
Index