Nuprl Lemma : eclass2_local
∀[Info,B,C:Type]. ∀[X:EClass(B ⟶ bag(C))]. ∀[Y:EClass(B)].
LocalClass(X) ⇒ LocalClass(Y) ⇒ LocalClass((X o Y)) supposing valueall-type(C)
Proof
Definitions occuring in Statement :
eclass2: (X o Y),
local-class: LocalClass(X),
eclass: EClass(A[eo; e]),
valueall-type: valueall-type(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
bag: bag(T)
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,
so_lambda: λ2x y.t[x; y],
subtype_rel: A ⊆r B,
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[X:EClass(B {}\mrightarrow{} bag(C))]. \mforall{}[Y:EClass(B)].
LocalClass(X) {}\mRightarrow{} LocalClass(Y) {}\mRightarrow{} LocalClass((X o Y)) supposing valueall-type(C)
Date html generated:
2016_05_17-AM-09_04_56
Last ObjectModification:
2015_12_29-PM-03_36_40
Theory : local!classes
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