Nuprl Lemma : simple-loc-comb-2-classrel-weak
∀[Info,A,B,C:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
(v ∈ lifting-loc-2(f) o (Loc,X, Y)(e) ⇐⇒ ↓∃a:A. ∃b:B. (a ∈ X(e) ∧ b ∈ Y(e) ∧ (v = (f loc(e) a b) ∈ C)))
Proof
Definitions occuring in Statement :
lifting-loc-2: lifting-loc-2(f),
simple-loc-comb-2: F o (Loc,X, Y),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
iff: P ⇐⇒ Q,
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
uiff: uiff(P;Q),
implies: P ⇒ Q,
uimplies: b supposing a,
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
exists: ∃x:A. B[x],
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)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E].
\mforall{}[v:C].
(v \mmember{} lifting-loc-2(f) o (Loc,X, Y)(e)
\mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}a:A. \mexists{}b:B. (a \mmember{} X(e) \mwedge{} b \mmember{} Y(e) \mwedge{} (v = (f loc(e) a b))))
Date html generated:
2016_05_17-AM-09_18_41
Last ObjectModification:
2015_12_29-PM-04_09_16
Theory : classrel!lemmas
Home
Index