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
Lemmas :
subtype_rel_dep_function,
event-ordering+_wf,
es-E_wf,
event-ordering+_subtype,
bag_wf,
subtype_rel_bag,
all_wf,
subtype_rel_wf
\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:
2015_07_17-PM-00_13_52
Last ObjectModification:
2015_01_28-AM-00_06_33
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