Nuprl Lemma : axiom-listunion

[A,B:Type]. ∀[L:Unit ⋃ (A × B)].  L ∈ Unit supposing isaxiom(L) tt


Proof




Definitions occuring in Statement :  b-union: A ⋃ B bfalse: ff btrue: tt bool: 𝔹 uimplies: supposing a uall: [x:A]. B[x] isaxiom: if Ax then otherwise b unit: Unit member: t ∈ T product: x:A × B[x] universe: Type equal: t ∈ T
Definitions unfolded in proof :  uall: [x:A]. B[x] uimplies: supposing a member: t ∈ T b-union: A ⋃ B tunion: x:A.B[x] bool: 𝔹 unit: Unit ifthenelse: if then else fi  pi2: snd(t) not: ¬A implies:  Q false: False
Lemmas referenced :  bool_wf btrue_wf bfalse_wf b-union_wf unit_wf2 btrue_neq_bfalse
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  cut sqequalHypSubstitution imageElimination productElimination thin unionElimination equalityElimination sqequalRule hypothesisEquality hypothesis Error :equalityIsType3,  Error :universeIsType,  introduction extract_by_obid baseClosed isectElimination productEquality Error :inhabitedIsType,  universeEquality equalitySymmetry independent_functionElimination voidElimination

Latex:
\mforall{}[A,B:Type].  \mforall{}[L:Unit  \mcup{}  (A  \mtimes{}  B)].    L  \mmember{}  Unit  supposing  isaxiom(L)  =  tt



Date html generated: 2019_06_20-PM-00_38_05
Last ObjectModification: 2018_10_06-AM-11_20_39

Theory : list_0


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