Nuprl Lemma : uniform-continuity-pi2_wf

`∀[T:Type]. ∀[F:(ℕ ⟶ 𝔹) ⟶ T]. ∀[n:ℕ].  (ucB(T;F;n) ∈ Type)`

Proof

Definitions occuring in Statement :  uniform-continuity-pi2: `ucB(T;F;n)` nat: `ℕ` bool: `𝔹` uall: `∀[x:A]. B[x]` member: `t ∈ T` function: `x:A ⟶ B[x]` universe: `Type`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` uniform-continuity-pi2: `ucB(T;F;n)` nat: `ℕ` so_lambda: `λ2x.t[x]` so_apply: `x[s]` all: `∀x:A. B[x]` prop: `ℙ`
Lemmas referenced :  all_wf int_seg_wf bool_wf equal_wf ext2Cantor_wf btrue_wf bfalse_wf nat_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalRule lemma_by_obid sqequalHypSubstitution isectElimination thin functionEquality natural_numberEquality setElimination rename hypothesisEquality hypothesis lambdaEquality applyEquality axiomEquality equalityTransitivity equalitySymmetry isect_memberEquality because_Cache universeEquality

Latex:
\mforall{}[T:Type].  \mforall{}[F:(\mBbbN{}  {}\mrightarrow{}  \mBbbB{})  {}\mrightarrow{}  T].  \mforall{}[n:\mBbbN{}].    (ucB(T;F;n)  \mmember{}  Type)

Date html generated: 2016_05_14-PM-09_38_28
Last ObjectModification: 2015_12_26-PM-09_49_22

Theory : continuity

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