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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