Nuprl Lemma : uniform-continuity-pi-pi_wf
∀[T:Type]. ∀[F:(ℕ ⟶ 𝔹) ⟶ T]. ∀[n:ℕ]. (ucpB(T;F;n) ∈ Type)
Proof
Definitions occuring in Statement :
uniform-continuity-pi-pi: ucpB(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-pi-pi: ucpB(T;F;n),
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
so_apply: x[s],
all: ∀x:A. B[x]
Lemmas referenced :
uniform-continuity-pi_wf,
all_wf,
nat_wf,
le_wf,
bool_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
productEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
lambdaEquality,
functionEquality,
setElimination,
rename,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} \mBbbB{}) {}\mrightarrow{} T]. \mforall{}[n:\mBbbN{}]. (ucpB(T;F;n) \mmember{} Type)
Date html generated:
2016_05_14-PM-09_39_00
Last ObjectModification:
2015_12_26-PM-09_49_13
Theory : continuity
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