Nuprl Lemma : simple-loc-comb-2-concat-loc-bounded
∀[Info,A,B,C:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ bag(C)]. ∀[X:EClass(A)]. ∀[Y:EClass(B)].
((LocBounded(A;X) ∨ LocBounded(B;Y)) ⇒ LocBounded(C;f@Loc o (Loc,X, Y)))
Proof
Definitions occuring in Statement :
concat-lifting-loc-2: f@Loc,
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,
bag: bag(T)
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{} bag(C)]. \mforall{}[X:EClass(A)]. \mforall{}[Y:EClass(B)].
((LocBounded(A;X) \mvee{} LocBounded(B;Y)) {}\mRightarrow{} LocBounded(C;f@Loc o (Loc,X, Y)))
Date html generated:
2016_05_17-AM-09_21_02
Last ObjectModification:
2016_01_17-PM-11_12_11
Theory : classrel!lemmas
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