Nuprl Lemma : non-pair-listunion

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


Proof




Definitions occuring in Statement :  b-union: A ⋃ B bfalse: ff btrue: tt bool: 𝔹 uimplies: supposing a uall: [x:A]. B[x] ispair: if is pair 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 prop:
Lemmas referenced :  btrue_neq_bfalse equal_wf bool_wf ispair_wf_listunion bfalse_wf b-union_wf unit_wf2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation cut sqequalHypSubstitution imageElimination productElimination thin unionElimination equalityElimination sqequalRule axiomEquality equalityTransitivity hypothesis equalitySymmetry lemma_by_obid independent_functionElimination voidElimination isectElimination hypothesisEquality productEquality universeEquality

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



Date html generated: 2016_05_15-PM-10_09_30
Last ObjectModification: 2015_12_27-PM-05_59_29

Theory : eval!all


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