Nuprl Lemma : bind-class_local
∀[Info,A,B:Type].
∀[X:EClass(A)]. ∀[Y:A ⟶ EClass(B)]. (LocalClass(X) ⇒ (∀a:A. LocalClass(Y[a])) ⇒ LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Proof
Definitions occuring in Statement :
bind-class: X >x> Y[x],
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
valueall-type: valueall-type(T),
has-value: (a)↓,
prop: ℙ,
implies: P ⇒ Q,
all: ∀x:A. B[x],
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,B:Type].
\mforall{}[X:EClass(A)]. \mforall{}[Y:A {}\mrightarrow{} EClass(B)].
(LocalClass(X) {}\mRightarrow{} (\mforall{}a:A. LocalClass(Y[a])) {}\mRightarrow{} LocalClass(X >a> Y[a]))
supposing valueall-type(B)
Date html generated:
2016_05_17-AM-09_06_54
Last ObjectModification:
2015_12_29-PM-03_36_10
Theory : local!classes
Home
Index