Nuprl Lemma : tunion_wf
∀[A:Type]. ∀[B:A ⟶ Type]. (⋃x:A.B[x] ∈ Type)
Proof
Definitions occuring in Statement :
tunion: ⋃x:A.B[x],
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
tunion: ⋃x:A.B[x],
so_apply: x[s]
Lemmas referenced :
image-type_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
productEquality,
hypothesisEquality,
applyEquality,
baseClosed,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
cumulativity,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[A:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. (\mcup{}x:A.B[x] \mmember{} Type)
Date html generated:
2016_05_13-PM-03_06_35
Last ObjectModification:
2016_01_06-PM-05_29_05
Theory : core_2
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