Nuprl Lemma : es-interface-filter_wf
∀[Info,A:Type]. ∀[X:EClass(A)]. ∀[P:A ⟶ 𝔹]. (X|a.P[a] ∈ EClass({a:A| ↑P[a]} ))
Proof
Definitions occuring in Statement :
es-interface-filter: X|a.P[a]
,
eclass: EClass(A[eo; e])
,
assert: ↑b
,
bool: 𝔹
,
uall: ∀[x:A]. B[x]
,
so_apply: x[s]
,
member: t ∈ T
,
set: {x:A| B[x]}
,
function: x:A ⟶ B[x]
,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
es-interface-filter: X|a.P[a]
,
eclass: EClass(A[eo; e])
,
eclass-compose1: f o X
,
subtype_rel: A ⊆r B
,
all: ∀x:A. B[x]
,
implies: P
⇒ Q
,
bool: 𝔹
,
unit: Unit
,
it: ⋅
,
btrue: tt
,
ifthenelse: if b then t else f fi
,
uiff: uiff(P;Q)
,
and: P ∧ Q
,
uimplies: b supposing a
,
so_lambda: λ2x.t[x]
,
so_apply: x[s]
,
bfalse: ff
,
exists: ∃x:A. B[x]
,
prop: ℙ
,
or: P ∨ Q
,
sq_type: SQType(T)
,
guard: {T}
,
bnot: ¬bb
,
assert: ↑b
,
false: False
,
so_lambda: λ2x y.t[x; y]
,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A:Type]. \mforall{}[X:EClass(A)]. \mforall{}[P:A {}\mrightarrow{} \mBbbB{}]. (X|a.P[a] \mmember{} EClass(\{a:A| \muparrow{}P[a]\} ))
Date html generated:
2016_05_16-PM-10_51_32
Last ObjectModification:
2015_12_29-AM-10_47_17
Theory : event-ordering
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