Nuprl Lemma : simple-loc-comb-2-loc-bounded
∀[Info,A,B,C:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
  ((LocBounded(A;X) ∨ LocBounded(B;Y)) 
⇒ LocBounded(C;lifting-loc-2(f) o (Loc,X, Y)))
Proof
Definitions occuring in Statement : 
lifting-loc-2: lifting-loc-2(f)
, 
simple-loc-comb-2: F o (Loc,X, Y)
, 
loc-bounded-class: LocBounded(T;X)
, 
eclass: EClass(A[eo; e])
, 
Id: Id
, 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
loc-bounded-class: LocBounded(T;X)
, 
class-loc-bound: class-loc-bound{i:l}(Info;T;X;L)
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
squash: ↓T
, 
subtype_rel: A ⊆r B
, 
sq_stable: SqStable(P)
, 
bag-member: x ↓∈ bs
, 
prop: ℙ
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B,C:Type].  \mforall{}[f:Id  {}\mrightarrow{}  A  {}\mrightarrow{}  B  {}\mrightarrow{}  C].  \mforall{}[X:EClass(A)].  \mforall{}[Y:EClass(B)].
    ((LocBounded(A;X)  \mvee{}  LocBounded(B;Y))  {}\mRightarrow{}  LocBounded(C;lifting-loc-2(f)  o  (Loc,X,  Y)))
Date html generated:
2016_05_17-AM-09_18_43
Last ObjectModification:
2016_01_17-PM-11_13_04
Theory : classrel!lemmas
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