Nuprl Lemma : inl_equal
∀[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 :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
outl: outl(x),
prop: ℙ,
isl: isl(x),
assert: ↑b,
ifthenelse: if b then t else f fi ,
btrue: tt,
true: True
Lemmas referenced :
and_wf,
equal_wf,
outl_wf,
assert_wf,
isl_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
hypothesisEquality,
equalitySymmetry,
dependent_set_memberEquality,
hypothesis,
equalityTransitivity,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
unionEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
independent_isectElimination,
promote_hyp,
hyp_replacement,
Error :applyLambdaEquality,
natural_numberEquality,
setEquality,
cumulativity,
inlEquality,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[x,y:A]. uiff((inl x) = (inl y);x = y)
Date html generated:
2016_10_25-AM-10_50_45
Last ObjectModification:
2016_07_12-AM-06_59_36
Theory : general
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