Nuprl Lemma : strong-continuous-product

[F,G:Type ⟶ Type].  (Continuous+(T.F[T] × G[T])) supposing (Continuous+(T.G[T]) and Continuous+(T.F[T]))


Definitions occuring in Statement :  strong-type-continuous: Continuous+(T.F[T]) uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] function: x:A ⟶ B[x] product: x:A × B[x] universe: Type
Definitions unfolded in proof :  so_apply: x[s] uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a strong-type-continuous: Continuous+(T.F[T]) ext-eq: A ≡ B and: P ∧ Q subtype_rel: A ⊆B prop: so_lambda: λ2x.t[x] nat: le: A ≤ B less_than': less_than'(a;b) false: False not: ¬A implies:  Q all: x:A. B[x] pi1: fst(t) pi2: snd(t)
Lemmas referenced :  nat_wf strong-type-continuous_wf pi1_wf pi2_wf false_wf le_wf equal_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut independent_pairFormation lambdaEquality isectEquality extract_by_obid hypothesis productEquality applyEquality functionExtensionality hypothesisEquality universeEquality thin isect_memberEquality productElimination independent_pairEquality sqequalHypSubstitution isectElimination equalityTransitivity equalitySymmetry because_Cache axiomEquality functionEquality cumulativity dependent_set_memberEquality natural_numberEquality lambdaFormation dependent_functionElimination independent_functionElimination

\mforall{}[F,G:Type  {}\mrightarrow{}  Type].
    (Continuous+(T.F[T]  \mtimes{}  G[T]))  supposing  (Continuous+(T.G[T])  and  Continuous+(T.F[T]))

Date html generated: 2017_04_14-AM-07_36_21
Last ObjectModification: 2017_02_27-PM-03_08_39

Theory : subtype_1

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