Nuprl Lemma : isaxiom_wf_listunion

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

Proof

Definitions occuring in Statement :  b-union: A ⋃ B bfalse: ff btrue: tt bool: 𝔹 uall: [x:A]. B[x] isaxiom: if Ax 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 :  btrue_wf bfalse_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)].    (isaxiom(L)  \mmember{}  \mBbbB{})

Date html generated: 2016_05_14-AM-06_25_10
Last ObjectModification: 2015_12_26-PM-00_42_39

Theory : list_0

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