Nuprl Lemma : fset-antichain-singleton
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. (↑fset-antichain(eq;{s}))
Proof
Definitions occuring in Statement :
fset-antichain: fset-antichain(eq;ac),
fset-singleton: {x},
fset: fset(T),
deq: EqDecider(T),
assert: ↑b,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
f-proper-subset: xs ⊆≠ ys
Lemmas referenced :
assert-fset-antichain,
fset-singleton_wf,
fset_wf,
f-proper-subset_wf,
fset-member_wf,
deq-fset_wf,
assert_witness,
fset-antichain_wf,
deq_wf,
member-fset-singleton
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
lambdaFormation,
independent_functionElimination,
voidElimination,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. (\muparrow{}fset-antichain(eq;\{s\}))
Date html generated:
2016_05_14-PM-03_42_47
Last ObjectModification:
2015_12_26-PM-06_39_35
Theory : finite!sets
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