Nuprl Lemma : strong-continuous-union

[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] union: left right 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] isl: isl(x) outl: outl(x) outr: outr(x) ifthenelse: if then else fi  btrue: tt bfalse: ff bool: 𝔹 unit: Unit it: uiff: uiff(P;Q)
Lemmas referenced :  nat_wf strong-type-continuous_wf subtype_rel_union false_wf le_wf equal_wf bool_wf eqtt_to_assert btrue_wf bfalse_wf outl_wf assert_wf isl_wf member_wf btrue_neq_bfalse equal-wf-T-base
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut independent_pairFormation lambdaEquality isectEquality extract_by_obid hypothesis unionEquality applyEquality functionExtensionality hypothesisEquality universeEquality isect_memberEquality sqequalHypSubstitution productElimination thin independent_pairEquality axiomEquality functionEquality cumulativity isectElimination because_Cache equalityTransitivity equalitySymmetry independent_isectElimination dependent_set_memberEquality natural_numberEquality lambdaFormation unionElimination dependent_functionElimination independent_functionElimination equalityElimination inlEquality inrEquality hyp_replacement applyLambdaEquality voidElimination baseClosed

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

Date html generated: 2017_04_14-AM-07_36_32
Last ObjectModification: 2017_02_27-PM-03_09_13

Theory : subtype_1

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