Nuprl Lemma : qv-convex_wf
∀[S:(ℚ List) ⟶ ℙ]. (qv-convex(p.S[p]) ∈ ℙ)
Proof
Definitions occuring in Statement :
qv-convex: qv-convex(p.S[p]),
rationals: ℚ,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qv-convex: qv-convex(p.S[p]),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
top: Top,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
list_wf,
rationals_wf,
equal_wf,
qv-dim_wf,
subtype_rel_list,
top_wf,
qle_wf,
int-subtype-rationals,
qv-add_wf,
qv-mul_wf,
qsub_wf,
dim-qv-mul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
because_Cache,
functionEquality,
intEquality,
hypothesisEquality,
applyEquality,
independent_isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
functionExtensionality,
universeEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity
Latex:
\mforall{}[S:(\mBbbQ{} List) {}\mrightarrow{} \mBbbP{}]. (qv-convex(p.S[p]) \mmember{} \mBbbP{})
Date html generated:
2018_05_22-AM-00_20_25
Last ObjectModification:
2017_07_26-PM-06_55_01
Theory : rationals
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