Nuprl Lemma : setrel_wf
∀[R:coSet{i:l}]. (setrel(R) ∈ coSet{i:l} ⟶ coSet{i:l} ⟶ ℙ)
Proof
Definitions occuring in Statement :
setrel: setrel(R),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
setrel: setrel(R),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
orderedpairset_wf,
setmem_wf
Rules used in proof :
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesis,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
lambdaEquality,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[R:coSet\{i:l\}]. (setrel(R) \mmember{} coSet\{i:l\} {}\mrightarrow{} coSet\{i:l\} {}\mrightarrow{} \mBbbP{})
Date html generated:
2018_07_29-AM-10_06_28
Last ObjectModification:
2018_07_20-AM-11_32_51
Theory : constructive!set!theory
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