Nuprl Lemma : fset-antichain_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[ac:fset(fset(T))]. (fset-antichain(eq;ac) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-antichain: fset-antichain(eq;ac),
fset: fset(T),
deq: EqDecider(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-antichain: fset-antichain(eq;ac),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
fset-pairwise_wf,
fset_wf,
bnot_wf,
f-proper-subset-dec_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[ac:fset(fset(T))]. (fset-antichain(eq;ac) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_42_38
Last ObjectModification:
2015_12_26-PM-06_39_33
Theory : finite!sets
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