Nuprl Lemma : fset-minimal_wf
∀[T:Type]. ∀[less:T ⟶ T ⟶ 𝔹]. ∀[s:fset(T)]. ∀[a:T]. (fset-minimal(x,y.less[x;y];s;a) ∈ 𝔹)
Proof
Definitions occuring in Statement :
fset-minimal: fset-minimal(x,y.less[x; y];s;a),
fset: fset(T),
bool: 𝔹,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset-minimal: fset-minimal(x,y.less[x; y];s;a),
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
fset-null_wf,
fset-filter_wf,
fset_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
applyEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[less:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbB{}]. \mforall{}[s:fset(T)]. \mforall{}[a:T]. (fset-minimal(x,y.less[x;y];s;a) \mmember{} \mBbbB{})
Date html generated:
2016_05_14-PM-03_47_27
Last ObjectModification:
2015_12_26-PM-06_36_41
Theory : finite!sets
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