Nuprl Lemma : uniform-continuity-pi2-dec-ext
∀T:Type. ∀F:(ℕ ⟶ 𝔹) ⟶ T. ∀n:ℕ. ((∀x,y:T. Dec(x = y ∈ T)) ⇒ Dec(ucB(T;F;n)))
Proof
Definitions occuring in Statement :
uniform-continuity-pi2: ucB(T;F;n),
nat: ℕ,
bool: 𝔹,
decidable: Dec(P),
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
btrue: tt,
it: ⋅,
bfalse: ff,
ifthenelse: if b then t else f fi ,
uniform-continuity-pi2-dec,
decidable__not,
decidable__implies,
decidable__false,
any: any x
Lemmas referenced :
uniform-continuity-pi2-dec,
decidable__not,
decidable__implies,
decidable__false
Rules used in proof :
introduction,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
instantiate,
extract_by_obid,
hypothesis,
sqequalRule,
thin,
sqequalHypSubstitution,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}T:Type. \mforall{}F:(\mBbbN{} {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} T. \mforall{}n:\mBbbN{}. ((\mforall{}x,y:T. Dec(x = y)) {}\mRightarrow{} Dec(ucB(T;F;n)))
Date html generated:
2018_05_21-PM-01_19_55
Last ObjectModification:
2018_05_19-AM-06_32_36
Theory : continuity
Home
Index