Nuprl Lemma : l_exists-interface-predecessors
∀[Info:Type]
∀es:EO+(Info). ∀X:EClass(Top). ∀[P:E(X) ⟶ ℙ]. ∀e:E. ((∃e'∈≤(X)(e). P[e']) ⇐⇒ ∃e':E(X). (e' ≤loc e ∧ P[e']))
Proof
Definitions occuring in Statement :
es-interface-predecessors: ≤(X)(e),
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
l_exists: (∃x∈L. P[x]),
uall: ∀[x:A]. B[x],
top: Top,
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
exists: ∃x:A. B[x],
member: t ∈ T,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B,
es-E-interface: E(X),
so_apply: x[s],
so_lambda: λ2x.t[x],
rev_implies: P ⇐ Q,
uimplies: b supposing a,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info). \mforall{}X:EClass(Top).
\mforall{}[P:E(X) {}\mrightarrow{} \mBbbP{}]. \mforall{}e:E. ((\mexists{}e'\mmember{}\mleq{}(X)(e). P[e']) \mLeftarrow{}{}\mRightarrow{} \mexists{}e':E(X). (e' \mleq{}loc e \mwedge{} P[e']))
Date html generated:
2016_05_17-AM-07_01_33
Last ObjectModification:
2015_12_29-AM-00_15_07
Theory : event-ordering
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