Nuprl Lemma : dep-eclass_subtype_rel
∀[T:Type]. ∀[A,B:es:EO+(T) ⟶ e:E ⟶ Type].
EClass(A[es;e]) ⊆r EClass(B[es;e]) supposing ∀es:EO+(T). ∀e:E. (A[es;e] ⊆r B[es;e])
Proof
Definitions occuring in Statement :
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
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[s1;s2],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ
Latex:
\mforall{}[T:Type]. \mforall{}[A,B:es:EO+(T) {}\mrightarrow{} e:E {}\mrightarrow{} Type].
EClass(A[es;e]) \msubseteq{}r EClass(B[es;e]) supposing \mforall{}es:EO+(T). \mforall{}e:E. (A[es;e] \msubseteq{}r B[es;e])
Date html generated:
2016_05_16-PM-01_26_39
Last ObjectModification:
2015_12_29-PM-02_03_36
Theory : event-ordering
Home
Index