Nuprl Lemma : atom_eq_wf
∀[T:Type]. ∀[a,b:T]. ∀[x,y:Atom]. (if x=y then a else b fi ∈ T)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
member: t ∈ T,
atom_eq: if a=b then c else d fi ,
atom: Atom,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
false: False,
implies: P ⇒ Q,
not: ¬A
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
atom_eqEquality,
hypothesisEquality,
sqequalHypSubstitution,
hypothesis,
sqequalRule,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
atomEquality,
isect_memberEquality,
isectElimination,
thin,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[a,b:T]. \mforall{}[x,y:Atom]. (if x=y then a else b fi \mmember{} T)
Date html generated:
2019_06_20-AM-11_18_27
Last ObjectModification:
2018_09_13-AM-01_12_24
Theory : core_2
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