Nuprl Lemma : inl_eq_inr
∀[A,B:Type]. ∀[x:A]. ∀[y:B]. uiff((inl x) = (inr y ) ∈ (A + B);False)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
false: False,
inr: inr x ,
inl: inl 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,
false: False,
isl: isl(x),
prop: ℙ,
not: ¬A,
implies: P ⇒ Q
Lemmas referenced :
btrue_wf,
bfalse_wf,
and_wf,
equal_wf,
isl_wf,
btrue_neq_bfalse,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
lemma_by_obid,
hypothesis,
equalitySymmetry,
dependent_set_memberEquality,
equalityTransitivity,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
hypothesisEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
setEquality,
independent_functionElimination,
voidElimination,
because_Cache,
inlEquality,
inrEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x:A]. \mforall{}[y:B]. uiff((inl x) = (inr y );False)
Date html generated:
2016_05_15-PM-03_58_33
Last ObjectModification:
2015_12_27-PM-03_06_41
Theory : general
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