Nuprl Lemma : inr-one-one
∀[A,B:Type]. ∀[x,y:B]. uiff((inr x ) = (inr y ) ∈ (A + B);x = y ∈ B)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
inr: inr x ,
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
prop: ℙ
Lemmas referenced :
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
sqequalRule,
applyEquality,
lambdaEquality,
unionElimination,
thin,
hypothesisEquality,
unionEquality,
hypothesis,
lemma_by_obid,
isectElimination,
inrEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:B]. uiff((inr x ) = (inr y );x = y)
Date html generated:
2016_05_13-PM-03_20_14
Last ObjectModification:
2015_12_26-AM-09_10_58
Theory : union
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