Nuprl Lemma : set-relation_wf
∀[R:Set{i:l} ⟶ Set{i:l} ⟶ ℙ']. (SetRelation(R) ∈ ℙ')
Proof
Definitions occuring in Statement :
set-relation: SetRelation(R),
Set: Set{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
so_lambda: λ2x.t[x],
set-relation: SetRelation(R),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
seteq_wf,
Set_wf,
all_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
hypothesisEquality,
cumulativity,
functionEquality,
lambdaEquality,
hypothesis,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
instantiate,
thin,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[R:Set\{i:l\} {}\mrightarrow{} Set\{i:l\} {}\mrightarrow{} \mBbbP{}']. (SetRelation(R) \mmember{} \mBbbP{}')
Date html generated:
2018_05_29-PM-01_51_41
Last ObjectModification:
2018_05_25-PM-01_59_40
Theory : constructive!set!theory
Home
Index