### Nuprl Lemma : uniform-continuity-pi2-dec

`∀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 :  all: `∀x:A. B[x]` implies: `P `` Q` uniform-continuity-pi2: `ucB(T;F;n)` member: `t ∈ T` prop: `ℙ` uall: `∀[x:A]. B[x]` so_lambda: `λ2x.t[x]` so_apply: `x[s]` nat: `ℕ` subtype_rel: `A ⊆r B` exists: `∃x:A. B[x]` decidable: `Dec(P)` or: `P ∨ Q` not: `¬A` guard: `{T}` false: `False`
Lemmas referenced :  all_wf decidable_wf equal_wf nat_wf bool_wf decidable__all_int_seg int_seg_wf decidable__bool decidable__not ext2Cantor_wf btrue_wf bfalse_wf simple-finite-cantor-decider_wf not_wf exists_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity lambdaFormation cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality hypothesis functionEquality universeEquality instantiate dependent_functionElimination natural_numberEquality setElimination rename independent_functionElimination applyEquality introduction unionElimination productElimination inrFormation inlFormation dependent_pairFormation voidElimination

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: 2016_05_14-PM-09_38_35
Last ObjectModification: 2015_12_26-PM-09_49_19

Theory : continuity

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