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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