Nuprl Lemma : p-lift_wf
∀[A,B:Type]. ∀[P:A ⟶ ℙ]. ∀[d:x:A ⟶ Dec(P[x])]. ∀[f:{x:A| P[x]}  ⟶ B].  (p-lift(d;f) ∈ A ⟶ (B + Top))
Proof
Definitions occuring in Statement : 
p-lift: p-lift(d;f)
, 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
prop: ℙ
, 
so_apply: x[s]
, 
member: t ∈ T
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
union: left + right
, 
universe: Type
Definitions unfolded in proof : 
p-lift: p-lift(d;f)
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
subtype_rel: A ⊆r B
, 
top: Top
, 
prop: ℙ
Lemmas referenced : 
decidable_wf, 
top_wf, 
equal_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
lambdaEquality, 
applyEquality, 
hypothesisEquality, 
thin, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
hypothesis, 
lambdaFormation, 
unionElimination, 
inlEquality, 
dependent_set_memberEquality, 
because_Cache, 
inrEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
cumulativity, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality, 
functionEquality, 
setEquality, 
universeEquality
Latex:
\mforall{}[A,B:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbP{}].  \mforall{}[d:x:A  {}\mrightarrow{}  Dec(P[x])].  \mforall{}[f:\{x:A|  P[x]\}    {}\mrightarrow{}  B].
    (p-lift(d;f)  \mmember{}  A  {}\mrightarrow{}  (B  +  Top))
Date html generated:
2016_05_15-PM-03_29_16
Last ObjectModification:
2015_12_27-PM-01_09_57
Theory : general
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