Nuprl Lemma : up-set_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[le:T ⟶ T ⟶ ℙ]. ∀[s:fset(T)]. (up-set(T;eq;x,y.le[x;y];s) ∈ ℙ)
Proof
Definitions occuring in Statement :
up-set: up-set(T;eq;x,y.le[x; y];s),
fset: fset(T),
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
prop: ℙ,
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,
up-set: up-set(T;eq;x,y.le[x; y];s),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s1;s2],
so_apply: x[s]
Lemmas referenced :
all_wf,
fset-member_wf,
fset_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
functionEquality,
hypothesis,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
cumulativity,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[le:T {}\mrightarrow{} T {}\mrightarrow{} \mBbbP{}]. \mforall{}[s:fset(T)]. (up-set(T;eq;x,y.le[x;y];s) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-03_47_22
Last ObjectModification:
2015_12_26-PM-06_36_45
Theory : finite!sets
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