Nuprl Lemma : productset_wf
∀[a,b:coSet{i:l}]. (a x b ∈ coSet{i:l})
Proof
Definitions occuring in Statement :
productset: a x b,
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
mk-coset: mk-coset(T;f),
productset: a x b,
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
coSet_wf,
orderedpairset_wf,
mk-coset_wf,
coSet_subtype,
subtype_coSet
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
spreadEquality,
lambdaEquality,
productEquality,
isectElimination,
thin,
productElimination,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:coSet\{i:l\}]. (a x b \mmember{} coSet\{i:l\})
Date html generated:
2018_07_29-AM-10_03_56
Last ObjectModification:
2018_07_18-PM-11_41_05
Theory : constructive!set!theory
Home
Index