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: uall: [x:A]. B[x] prop: 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: so_lambda: λ2x.t[x] prop: 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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