Nuprl Lemma : inl-one-one
∀[A,B:Type]. ∀[x,y:A]. uiff((inl x) = (inl y) ∈ (A + B);x = y ∈ A)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
inl: inl x,
union: left + right,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
prop: ℙ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
equal_wf
Rules used in proof :
universeEquality,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
isect_memberEquality,
independent_pairEquality,
productElimination,
because_Cache,
inlEquality,
cumulativity,
unionEquality,
isectElimination,
extract_by_obid,
hypothesis,
hypothesisEquality,
thin,
unionElimination,
applyLambdaEquality,
sqequalRule,
sqequalHypSubstitution,
independent_pairFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:A]. uiff((inl x) = (inl y);x = y)
Date html generated:
2018_05_21-PM-00_00_52
Last ObjectModification:
2017_12_11-PM-06_47_06
Theory : union
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