Nuprl Lemma : assert-deq-fset
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[x,y:fset(T)]. uiff(↑(deq-fset(eq) x y);x = y ∈ fset(T))
Proof
Definitions occuring in Statement :
deq-fset: deq-fset(eq),
fset: fset(T),
deq: EqDecider(T),
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
apply: f a,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
deq: EqDecider(T),
prop: ℙ,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
guard: {T},
subtype_rel: A ⊆r B,
sq_stable: SqStable(P),
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
deq-fset_wf,
deq_wf,
fset_wf,
equal_wf,
assert_wf,
assert_witness,
sq_stable__uiff,
sq_stable_from_decidable,
decidable__assert,
sq_stable__equal
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaFormation,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
independent_functionElimination,
applyEquality,
functionExtensionality,
because_Cache,
independent_pairFormation,
isect_memberFormation,
lambdaEquality,
sqequalRule,
universeEquality,
productElimination,
independent_pairEquality,
isect_memberEquality,
axiomEquality,
imageMemberEquality,
baseClosed,
imageElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[x,y:fset(T)]. uiff(\muparrow{}(deq-fset(eq) x y);x = y)
Date html generated:
2017_04_17-AM-09_20_18
Last ObjectModification:
2017_02_27-PM-05_23_14
Theory : finite!sets
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