Nuprl Lemma : simple-comb-2-classrel-weak
∀[Info,A,B,C:Type]. ∀[f:A ⟶ B ⟶ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
(v ∈ lifting-2(f)|X, Y|(e) ⇐⇒ ↓∃a:A. ∃b:B. ((v = (f a b) ∈ C) ∧ b ∈ Y(e) ∧ a ∈ X(e)))
Proof
Definitions occuring in Statement :
simple-comb-2: F|X, Y|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
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,
lifting-2: lifting-2(f)
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,
all: ∀x:A. B[x],
prop: ℙ,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,A,B,C:Type]. \mforall{}[f: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-2(f)|X, Y|(e) \mLeftarrow{}{}\mRightarrow{} \mdownarrow{}\mexists{}a:A. \mexists{}b:B. ((v = (f a b)) \mwedge{} b \mmember{} Y(e) \mwedge{} a \mmember{} X(e)))
Date html generated:
2016_05_17-AM-09_20_59
Last ObjectModification:
2015_12_29-PM-04_07_02
Theory : classrel!lemmas
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