Nuprl Lemma : bind-class-rel
∀[Info,T,S:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(T)]. ∀[Y:T ⟶ EClass(S)]. ∀[e:E]. ∀[v:S].
uiff(v ∈ X >u> Y[u](e);↓∃e':{e':E| e' ≤loc e } . ∃u:T. (u ∈ X(e') ∧ v ∈ Y[u](e)))
Proof
Definitions occuring in Statement :
bind-class: X >x> Y[x],
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
eo-forward: eo.e,
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
so_apply: x[s],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
bind-class: X >x> Y[x],
eclass: EClass(A[eo; e]),
exists: ∃x:A. B[x],
rev_uimplies: rev_uimplies(P;Q),
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
decidable: Dec(P),
or: P ∨ Q,
false: False,
not: ¬A
Latex:
\mforall{}[Info,T,S:Type]. \mforall{}[es:EO+(Info)]. \mforall{}[X:EClass(T)]. \mforall{}[Y:T {}\mrightarrow{} EClass(S)]. \mforall{}[e:E]. \mforall{}[v:S].
uiff(v \mmember{} X >u> Y[u](e);\mdownarrow{}\mexists{}e':\{e':E| e' \mleq{}loc e \} . \mexists{}u:T. (u \mmember{} X(e') \mwedge{} v \mmember{} Y[u](e)))
Date html generated:
2016_05_16-PM-02_30_01
Last ObjectModification:
2016_01_17-PM-07_34_10
Theory : event-ordering
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