Nuprl Lemma : set-sig-empty-prop
∀[Item:Type]. ∀[s:set-sig{i:l}(Item)]. ∀[x:Item]. (¬↑(set-sig-member(s) x set-sig-empty(s)))
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,
uall: ∀[x:A]. B[x],
not: ¬A,
apply: f a,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
set-sig: set-sig{i:l}(Item),
record+: record+,
record-select: r.x,
subtype_rel: A ⊆r B,
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
btrue: tt,
guard: {T},
so_lambda: λ2x.t[x],
so_apply: x[s],
all: ∀x:A. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
and: P ∧ Q,
or: P ∨ Q,
set-sig-member: set-sig-member(s),
set-sig-set: set-sig-set(s),
set-sig-empty: set-sig-empty(s),
squash: ↓T
Latex:
\mforall{}[Item:Type]. \mforall{}[s:set-sig\{i:l\}(Item)]. \mforall{}[x:Item]. (\mneg{}\muparrow{}(set-sig-member(s) x set-sig-empty(s)))
Date html generated:
2016_05_17-PM-01_44_19
Last ObjectModification:
2016_01_17-AM-11_37_42
Theory : datatype-signatures
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