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: b supposing a,
uall: ∀[x:A]. B[x],
isaxiom: if z = Ax then a otherwise b,
unit: Unit,
member: t ∈ T,
product: x:A × B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
b-union: A ⋃ B,
tunion: ⋃x:A.B[x],
bool: 𝔹,
unit: Unit,
ifthenelse: if b then t else f fi ,
pi2: snd(t),
not: ¬A,
implies: P ⇒ 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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