Nuprl Lemma : set-sig-singleton_wf
∀[Item:Type]. ∀[s:set-sig{i:l}(Item)]. (set-sig-singleton(s) ∈ Item ⟶ set-sig-set(s))
Proof
Definitions occuring in Statement :
set-sig-singleton: set-sig-singleton(s),
set-sig-set: set-sig-set(s),
set-sig: set-sig{i:l}(Item),
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
set-sig-singleton: set-sig-singleton(s),
set-sig-set: set-sig-set(s),
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,
implies: P ⇒ Q,
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
Latex:
\mforall{}[Item:Type]. \mforall{}[s:set-sig\{i:l\}(Item)]. (set-sig-singleton(s) \mmember{} Item {}\mrightarrow{} set-sig-set(s))
Date html generated:
2016_05_17-PM-01_44_26
Last ObjectModification:
2015_12_28-PM-08_52_36
Theory : datatype-signatures
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