Nuprl Lemma : dep-eclass_subtype_rel2
∀[T:Type]. ∀[A:EO+(T) ⟶ Type]. ∀[B:Type]. EClass(A[es]) ⊆r EClass(B) supposing ∀eo:EO+(T). (A[eo] ⊆r B)
Proof
Definitions occuring in Statement :
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
eclass: EClass(A[eo; e]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Latex:
\mforall{}[T:Type]. \mforall{}[A:EO+(T) {}\mrightarrow{} Type]. \mforall{}[B:Type].
EClass(A[es]) \msubseteq{}r EClass(B) supposing \mforall{}eo:EO+(T). (A[eo] \msubseteq{}r B)
Date html generated:
2016_05_16-PM-01_26_50
Last ObjectModification:
2015_12_29-PM-02_03_12
Theory : event-ordering
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