Nuprl Lemma : subtype-fpf-cap-void
∀[T,X:Type]. ∀[eq:EqDecider(X)]. ∀[f,g:x:X fp-> Type]. ∀[x:X]. f(x)?Void ⊆r g(x)?T supposing f ⊆ g
Proof
Definitions occuring in Statement :
fpf-sub: f ⊆ g,
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
void: Void,
universe: Type
Lemmas :
l_member_wf,
subtype_base_sq,
fpf_wf,
list_subtype_base,
list_wf,
product_subtype_base,
fpf-cap_wf,
deq_wf,
fpf-sub_wf,
squash_wf,
true_wf,
subtype_rel-equal,
bool_wf,
eqtt_to_assert,
assert_wf,
not_wf,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
fpf-dom_wf,
top_wf,
subtype-fpf2,
subtype_top,
equal-wf-base,
equal-wf-base-T,
equal-wf-T-base,
bnot_wf,
fpf-ap_wf
\mforall{}[T,X:Type]. \mforall{}[eq:EqDecider(X)]. \mforall{}[f,g:x:X fp-> Type]. \mforall{}[x:X]. f(x)?Void \msubseteq{}r g(x)?T supposing f \msubseteq{} g
Date html generated:
2015_07_17-AM-09_17_57
Last ObjectModification:
2015_01_28-AM-07_51_25
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