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
Definitions unfolded in proof :
alle-lt: ∀e<e'.P[e],
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top,
so_lambda: λ2x.t[x],
decidable: Dec(P),
or: P ∨ Q,
false: False,
not: ¬A,
so_apply: x[s],
cand: A c∧ B,
es-locl: (e <loc e'),
rev_implies: P ⇐ Q
Latex:
\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:
2016_05_16-PM-01_11_44
Last ObjectModification:
2015_12_29-PM-01_53_32
Theory : event-ordering
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