Nuprl Lemma : simple-loc-comb-1-classrel-weak
∀[Info,B,C:Type]. ∀[f:Id ⟶ B ⟶ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
(v ∈ lifting-loc-1(f)(Loc, X)(e) ⇐⇒ ↓∃b:B. (b ∈ X(e) ∧ (v = (f loc(e) b) ∈ C)))
Proof
Definitions occuring in Statement :
lifting-loc-1: lifting-loc-1(f),
simple-loc-comb-1: F(Loc, X),
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,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
rev_implies: P ⇐ Q,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[f:Id {}\mrightarrow{} B {}\mrightarrow{} C]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
(v \mmember{} lifting-loc-1(f)(Loc, X)(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} (v = (f loc(e) b))))
Date html generated:
2016_05_17-AM-09_18_17
Last ObjectModification:
2016_01_17-PM-11_13_11
Theory : classrel!lemmas
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