Nuprl Lemma : fpf-cap-void-subtype
∀[A:Type]. ∀[eq:EqDecider(A)]. ∀[ds:x:A fp-> Type]. ∀[x:A]. (ds(x)?Void ⊆r ds(x)?Top)
Proof
Definitions occuring in Statement :
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
top: Top,
void: Void,
universe: Type
Lemmas :
fpf_wf,
deq_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
subtype_top,
bool_wf,
subtype_rel_self,
fpf-ap_wf,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot
\mforall{}[A:Type]. \mforall{}[eq:EqDecider(A)]. \mforall{}[ds:x:A fp-> Type]. \mforall{}[x:A]. (ds(x)?Void \msubseteq{}r ds(x)?Top)
Date html generated:
2015_07_17-AM-09_17_55
Last ObjectModification:
2015_01_28-AM-07_50_26
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