Nuprl Lemma : productset_wf2
∀[a,b:Set{i:l}]. (a x b ∈ Set{i:l})
Proof
Definitions occuring in Statement :
productset: a x b,
Set: Set{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
mkset: {f[t] | t ∈ T},
productset: a x b,
Wsup: Wsup(a;b),
mk-set: f"(T),
subtype_rel: A ⊆r B,
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Set_wf,
orderedpairset_wf2,
mkset_wf,
set-subtype,
subtype-set
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
spreadEquality,
lambdaEquality,
productEquality,
isectElimination,
rename,
thin,
productElimination,
sqequalRule,
sqequalHypSubstitution,
applyEquality,
hypothesisEquality,
hypothesis,
extract_by_obid,
hypothesis_subsumption,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:Set\{i:l\}]. (a x b \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-10_03_59
Last ObjectModification:
2018_07_18-PM-11_41_16
Theory : constructive!set!theory
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