Nuprl Lemma : pairset_wf2
∀[a,b:Set{i:l}]. ({a,b} ∈ Set{i:l})
Proof
Definitions occuring in Statement :
pairset: {a,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},
pairset: {a,b},
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
Set_wf,
ifthenelse_wf,
bool_wf,
mkset_wf
Rules used in proof :
because_Cache,
isect_memberEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
hypothesisEquality,
instantiate,
lambdaEquality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
sqequalRule,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[a,b:Set\{i:l\}]. (\{a,b\} \mmember{} Set\{i:l\})
Date html generated:
2018_07_29-AM-09_59_32
Last ObjectModification:
2018_07_18-AM-11_07_43
Theory : constructive!set!theory
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