Nuprl Lemma : tunion-is-image
∀[A:Type]. ∀[B:A ⟶ Type]. (⋃a:A.B[a] ~ Image((a:A × B[a]),(λp.(snd(p)))))
Proof
Definitions occuring in Statement :
tunion: ⋃x:A.B[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
pi2: snd(t),
image-type: Image(T,f),
lambda: λx.A[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type,
sqequal: s ~ t
Definitions unfolded in proof :
tunion: ⋃x:A.B[x],
uall: ∀[x:A]. B[x],
member: t ∈ T
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalAxiom,
functionEquality,
cumulativity,
hypothesisEquality,
universeEquality,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (\mcup{}a:A.B[a] \msim{} Image((a:A \mtimes{} B[a]),(\mlambda{}p.(snd(p)))))
Date html generated:
2016_05_13-PM-03_19_38
Last ObjectModification:
2015_12_26-AM-09_07_43
Theory : subtype_0
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