Nuprl Lemma : eo-forward-alle-lt
∀Info:Type. ∀es:EO+(Info). ∀b:E. ∀e:{e:E| b ≤loc e } .
∀[P:{e':E| b ≤loc e' ∧ (e' <loc e)} ─→ ℙ]. (∀e'<e.P[e'] ⇐⇒ ∀e':E. (b ≤loc e' ⇒ (e' <loc e) ⇒ P[e']))
Proof
Definitions occuring in Statement :
eo-forward: eo.e,
event-ordering+: EO+(Info),
alle-lt: ∀e<e'.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-E: E,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ─→ B[x],
universe: Type
Lemmas :
member-eo-forward-E,
equal_wf,
Id_wf,
es-loc_wf,
event-ordering+_subtype,
eo-forward-locl,
es-locl_wf,
es-le_wf,
es-E_wf,
all_wf,
eo-forward_wf,
decidable__es-le,
eo-forward-E-member,
es-le-loc,
set_wf,
event-ordering+_wf
\mforall{}Info:Type. \mforall{}es:EO+(Info). \mforall{}b:E. \mforall{}e:\{e:E| b \mleq{}loc e \} .
\mforall{}[P:\{e':E| b \mleq{}loc e' \mwedge{} (e' <loc e)\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e'<e.P[e'] \mLeftarrow{}{}\mRightarrow{} \mforall{}e':E. (b \mleq{}loc e' {}\mRightarrow{} (e' <loc e) {}\mRightarrow{} P[e']))
Date html generated:
2015_07_17-PM-00_05_43
Last ObjectModification:
2015_01_28-AM-00_14_19
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