Nuprl Lemma : local-class-ap-member
∀[Info,A,T:Type]. ∀[X:T ⟶ EClass(A)]. ∀[prog:∀x:T. LocalClass(X x)]. ∀[x:T]. (prog x ∈ LocalClass(X x))
Proof
Definitions occuring in Statement :
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,T:Type]. \mforall{}[X:T {}\mrightarrow{} EClass(A)]. \mforall{}[prog:\mforall{}x:T. LocalClass(X x)]. \mforall{}[x:T].
(prog x \mmember{} LocalClass(X x))
Date html generated:
2016_05_16-PM-02_05_25
Last ObjectModification:
2015_12_29-PM-02_25_21
Theory : event-ordering
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