### Nuprl Lemma : ispair_wf_listunion

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

Proof

Definitions occuring in Statement :  b-union: A ⋃ B bfalse: ff btrue: tt bool: 𝔹 uall: [x:A]. B[x] ispair: if is pair then otherwise b unit: Unit member: t ∈ T product: x:A × B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T b-union: A ⋃ B tunion: x:A.B[x] bool: 𝔹 unit: Unit ifthenelse: if then else fi  pi2: snd(t)
Lemmas referenced :  bfalse_wf btrue_wf b-union_wf unit_wf2
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution imageElimination productElimination thin unionElimination equalityElimination sqequalRule lemma_by_obid hypothesis axiomEquality equalityTransitivity equalitySymmetry isectElimination productEquality hypothesisEquality isect_memberEquality because_Cache universeEquality

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

Date html generated: 2016_05_15-PM-10_09_26
Last ObjectModification: 2015_12_27-PM-05_59_34

Theory : eval!all

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