Nuprl Lemma : continuous-function

[A,B:Type ⟶ Type].  (Continuous(T.A[T] ⟶ B[T])) supposing (Continuous(T.B[T]) and Continuous+(T.A[T]))


Definitions occuring in Statement :  strong-type-continuous: Continuous+(T.F[T]) type-continuous: Continuous(T.F[T]) uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a type-continuous: Continuous(T.F[T]) subtype_rel: A ⊆B nat: le: A ≤ B and: P ∧ Q less_than': less_than'(a;b) false: False not: ¬A implies:  Q prop: so_apply: x[s] so_lambda: λ2x.t[x] all: x:A. B[x] strong-type-continuous: Continuous+(T.F[T]) ext-eq: A ≡ B
Lemmas referenced :  false_wf le_wf nat_wf type-continuous_wf strong-type-continuous_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lambdaEquality isectElimination dependent_set_memberEquality natural_numberEquality sqequalRule independent_pairFormation lambdaFormation hypothesis extract_by_obid sqequalHypSubstitution thin hypothesisEquality equalityTransitivity equalitySymmetry functionExtensionality applyEquality universeEquality isectEquality functionEquality axiomEquality cumulativity isect_memberEquality because_Cache dependent_functionElimination independent_functionElimination productElimination

\mforall{}[A,B:Type  {}\mrightarrow{}  Type].
    (Continuous(T.A[T]  {}\mrightarrow{}  B[T]))  supposing  (Continuous(T.B[T])  and  Continuous+(T.A[T]))

Date html generated: 2017_04_14-AM-07_36_18
Last ObjectModification: 2017_02_27-PM-03_08_40

Theory : subtype_1

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