Nuprl Lemma : less-member
∀[T:Type]. ∀[n,m:ℤ]. ∀[a,b:T]. (if (n) < (m) then a else b ∈ T)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
member: t ∈ T,
less: if (a) < (b) then c else d,
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
lessCases,
equalityTransitivity,
hypothesis,
equalitySymmetry,
sqequalRule,
thin,
sqequalHypSubstitution,
isectElimination,
axiomSqEquality,
extract_by_obid,
isect_memberEquality,
because_Cache,
voidElimination,
voidEquality,
axiomEquality,
intEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[n,m:\mBbbZ{}]. \mforall{}[a,b:T]. (if (n) < (m) then a else b \mmember{} T)
Date html generated:
2019_06_20-AM-11_18_44
Last ObjectModification:
2018_08_20-PM-09_28_05
Theory : core_2
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