Nuprl Lemma : respects-equality-set-trivial2
∀[T:Type]. ∀[P:T ⟶ ℙ]. respects-equality({x:T| P[x]} ;T)
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,
prop: ℙ,
so_apply: x[s],
squash: ↓T
Lemmas referenced :
istype-base
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
Error :lambdaFormation_alt,
hypothesis,
sqequalRule,
Error :equalityIstype,
because_Cache,
hypothesisEquality,
sqequalBase,
equalitySymmetry,
Error :setIsType,
Error :universeIsType,
applyEquality,
Error :inhabitedIsType,
extract_by_obid,
sqequalHypSubstitution,
Error :lambdaEquality_alt,
dependent_functionElimination,
thin,
axiomEquality,
Error :functionIsTypeImplies,
Error :functionIsType,
universeEquality,
Error :isect_memberEquality_alt,
isectElimination,
Error :isectIsTypeImplies,
applyLambdaEquality,
setElimination,
rename,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[T:Type]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. respects-equality(\{x:T| P[x]\} ;T)
Date html generated:
2019_06_20-AM-11_13_43
Last ObjectModification:
2018_12_02-PM-11_41_35
Theory : core_2
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