Nuprl Lemma : set-sig-empty-prop2
∀[Item:Type]. ∀[s:set-sig{i:l}(Item)]. ∀[x:Item]. uiff(↑(set-sig-member(s) x set-sig-empty(s));False)
Proof
Definitions occuring in Statement :
set-sig-empty: set-sig-empty(s),
set-sig-member: set-sig-member(s),
set-sig: set-sig{i:l}(Item),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
false: False,
apply: f a,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ
Latex:
\mforall{}[Item:Type]. \mforall{}[s:set-sig\{i:l\}(Item)]. \mforall{}[x:Item].
uiff(\muparrow{}(set-sig-member(s) x set-sig-empty(s));False)
Date html generated:
2016_05_17-PM-01_44_21
Last ObjectModification:
2015_12_28-PM-08_52_33
Theory : datatype-signatures
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