Nuprl Lemma : fset-singletons-equal
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x,y:T]. uiff({x} = {y} ∈ fset(T);x = y ∈ T)
Proof
Definitions occuring in Statement :
fset-singleton: {x},
fset: fset(T),
deq: EqDecider(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
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,
fset_wf,
fset-singleton_wf,
and_wf,
deq_wf,
member-fset-singleton,
fset-member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
equalitySymmetry,
dependent_set_memberEquality,
applyEquality,
lambdaEquality,
setElimination,
rename,
productElimination,
setEquality,
sqequalRule,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
because_Cache,
equalityTransitivity,
independent_isectElimination,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x,y:T]. uiff(\{x\} = \{y\};x = y)
Date html generated:
2016_10_21-AM-10_44_10
Last ObjectModification:
2016_07_12-AM-05_51_01
Theory : finite!sets
Home
Index