Nuprl Lemma : respects-equality-set-trivial
∀[T:Type]. ∀[P:T ⟶ ℙ].  respects-equality(T;{x:T| P[x]} )
Proof
Definitions occuring in Statement : 
respects-equality: respects-equality(S;T)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
respects-equality: respects-equality(S;T)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
prop: ℙ
, 
so_apply: x[s]
Lemmas referenced : 
istype-base
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
Error :lambdaFormation_alt, 
sqequalHypSubstitution, 
equalityTransitivity, 
hypothesis, 
equalitySymmetry, 
applyLambdaEquality, 
setElimination, 
thin, 
rename, 
sqequalRule, 
imageMemberEquality, 
hypothesisEquality, 
baseClosed, 
imageElimination, 
Error :dependent_set_memberEquality_alt, 
Error :universeIsType, 
applyEquality, 
Error :equalityIsType4, 
Error :setIsType, 
because_Cache, 
Error :inhabitedIsType, 
extract_by_obid, 
Error :lambdaEquality_alt, 
dependent_functionElimination, 
axiomEquality, 
Error :functionIsTypeImplies, 
Error :functionIsType, 
universeEquality, 
Error :isect_memberEquality_alt, 
isectElimination, 
Error :isectIsTypeImplies
Latex:
\mforall{}[T:Type].  \mforall{}[P:T  {}\mrightarrow{}  \mBbbP{}].    respects-equality(T;\{x:T|  P[x]\}  )
Date html generated:
2019_06_20-AM-11_13_42
Last ObjectModification:
2018_11_28-AM-11_09_49
Theory : core_2
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