Nuprl Lemma : fpf-dom-type
∀[X,Y:Type]. ∀[eq:EqDecider(Y)]. ∀[f:x:X fp-> Top]. ∀[x:Y]. (x ∈ X) supposing ((↑x ∈ dom(f)) and strong-subtype(X;Y))
Proof
Definitions occuring in Statement :
fpf-dom: x ∈ dom(f),
fpf: a:A fp-> B[a],
deq: EqDecider(T),
strong-subtype: strong-subtype(A;B),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
universe: Type
Lemmas :
strong-subtype-l_member-type,
fpf-domain_wf,
member-fpf-domain,
assert_wf,
fpf-dom_wf,
subtype-fpf3,
top_wf,
subtype_rel_self,
strong-subtype_wf,
fpf_wf,
deq_wf
\mforall{}[X,Y:Type]. \mforall{}[eq:EqDecider(Y)]. \mforall{}[f:x:X fp-> Top]. \mforall{}[x:Y].
(x \mmember{} X) supposing ((\muparrow{}x \mmember{} dom(f)) and strong-subtype(X;Y))
Date html generated:
2015_07_17-AM-09_16_00
Last ObjectModification:
2015_01_28-AM-07_52_31
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