Nuprl Lemma : decidable__exists-unit-ball-approx
∀k,n:ℕ.  ∀[P:unit-ball-approx(n;k) ⟶ ℙ]. ((∀p:unit-ball-approx(n;k). Dec(P[p])) 
⇒ Dec(∃p:unit-ball-approx(n;k). P[p]))
Proof
Definitions occuring in Statement : 
unit-ball-approx: unit-ball-approx(n;k)
, 
nat: ℕ
, 
decidable: Dec(P)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
exists: ∃x:A. B[x]
, 
implies: P 
⇒ Q
, 
function: x:A ⟶ B[x]
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
prop: ℙ
, 
exists: ∃x:A. B[x]
Lemmas referenced : 
unit-ball-ex-decider_wf, 
decidable_wf, 
unit-ball-approx_wf, 
istype-nat
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation_alt, 
isect_memberFormation_alt, 
rename, 
introduction, 
applyEquality, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
sqequalRule, 
lambdaEquality_alt, 
isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
isectIsType, 
because_Cache, 
functionIsType, 
universeIsType, 
productEquality, 
universeEquality, 
inhabitedIsType
Latex:
\mforall{}k,n:\mBbbN{}.
    \mforall{}[P:unit-ball-approx(n;k)  {}\mrightarrow{}  \mBbbP{}]
        ((\mforall{}p:unit-ball-approx(n;k).  Dec(P[p]))  {}\mRightarrow{}  Dec(\mexists{}p:unit-ball-approx(n;k).  P[p]))
Date html generated:
2019_10_30-AM-11_28_32
Last ObjectModification:
2019_07_30-AM-11_37_35
Theory : real!vectors
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