### 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]))`

Proof

Definitions occuring in Statement :  strong-type-continuous: `Continuous+(T.F[T])` uimplies: `b 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: `b supposing a` strong-type-continuous: `Continuous+(T.F[T])` ext-eq: `A ≡ B` and: `P ∧ Q` subtype_rel: `A ⊆r B` prop: `ℙ` so_lambda: `λ2x.t[x]` nat: `ℕ` le: `A ≤ B` less_than': `less_than'(a;b)` false: `False` not: `¬A` implies: `P `` Q` all: `∀x:A. B[x]` isl: `isl(x)` outl: `outl(x)` outr: `outr(x)` ifthenelse: `if b then t else f 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

Latex:
\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

Home Index