Nuprl Lemma : simple-comb1-concat-classrel
∀[Info,B,C:Type]. ∀[f:B ⟶ bag(C)]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ λa.concat-lifting1(f;a)|X|(e);↓∃b:B. (b ∈ X(e) ∧ v ↓∈ f b))
Proof
Definitions occuring in Statement :
simple-comb1: λx.F[x]|X|,
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
squash: ↓T,
and: P ∧ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
concat-lifting1: concat-lifting1(f;bag),
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
int_seg: {i..j-},
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
sq_type: SQType(T),
select: L[n],
cons: [a / b],
less_than: a < b,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
concat-lifting1: concat-lifting1(f;bag),
concat-lifting: concat-lifting(n;f;bags),
concat-lifting-list: concat-lifting-list(n;bags),
lifting-gen-list-rev: lifting-gen-list-rev(n;bags),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
btrue: tt,
cand: A c∧ B,
rev_uimplies: rev_uimplies(P;Q),
simple-comb1: λx.F[x]|X|
Latex:
\mforall{}[Info,B,C:Type]. \mforall{}[f:B {}\mrightarrow{} bag(C)]. \mforall{}[X:EClass(B)]. \mforall{}[es:EO+(Info)]. \mforall{}[e:E]. \mforall{}[v:C].
uiff(v \mmember{} \mlambda{}a.concat-lifting1(f;a)|X|(e);\mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} v \mdownarrow{}\mmember{} f b))
Date html generated:
2016_05_17-AM-09_19_44
Last ObjectModification:
2016_01_17-PM-11_15_19
Theory : classrel!lemmas
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