### 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

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