Nuprl Lemma : basic-strong-continuity_wf
∀[T:Type]. ∀[F:(ℕ ⟶ T) ⟶ ℕ]. (basic-strong-continuity(T;F) ∈ ℙ)
Proof
Definitions occuring in Statement :
basic-strong-continuity: basic-strong-continuity(T;F),
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
basic-strong-continuity: basic-strong-continuity(T;F),
bsc-body: bsc-body(F;M;f),
nat: ℕ,
so_lambda: λ2x.t[x],
prop: ℙ,
all: ∀x:A. B[x],
so_apply: x[s]
Lemmas referenced :
sq_exists_wf,
nat_wf,
int_seg_wf,
b-union_wf,
bsc-body_wf,
istype-nat,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
natural_numberEquality,
setElimination,
rename,
hypothesisEquality,
productEquality,
Error :lambdaEquality_alt,
Error :functionIsType,
Error :universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
Error :isect_memberEquality_alt,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
instantiate,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[F:(\mBbbN{} {}\mrightarrow{} T) {}\mrightarrow{} \mBbbN{}]. (basic-strong-continuity(T;F) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_50_12
Last ObjectModification:
2019_02_11-AM-11_18_18
Theory : continuity
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