Nuprl Lemma : non-axiom-listunion
∀[A,B:Type]. ∀[L:Unit ⋃ (A × B)]. L ∈ A × B supposing isaxiom(L) = ff
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,
prop: ℙ
Lemmas referenced :
btrue_neq_bfalse,
equal_wf,
bool_wf,
isaxiom_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,
hypothesis,
lemma_by_obid,
independent_functionElimination,
voidElimination,
independent_pairEquality,
hypothesisEquality,
isectElimination,
productEquality,
universeEquality
Latex:
\mforall{}[A,B:Type]. \mforall{}[L:Unit \mcup{} (A \mtimes{} B)]. L \mmember{} A \mtimes{} B supposing isaxiom(L) = ff
Date html generated:
2016_05_14-AM-06_25_12
Last ObjectModification:
2015_12_26-PM-00_42_39
Theory : list_0
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