Nuprl Lemma : simple-loc-comb1-classrel
∀[Info,B,C:Type]. ∀[f:Id ⟶ B ⟶ C]. ∀[X:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ simple-loc-comb1(l,a.lifting1-loc(f;l;a);X)(e);↓∃b:B. (b ∈ X(e) ∧ (v = (f loc(e) b) ∈ C)))
Proof
Definitions occuring in Statement :
lifting1-loc: lifting1-loc(f;loc;b),
simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-loc: loc(e),
es-E: E,
Id: Id,
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,
equal: s = t ∈ T
Definitions unfolded in proof :
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
classrel: v ∈ X(e),
bag-member: x ↓∈ bs,
nat: ℕ,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
int_seg: {i..j-},
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,
true: True,
funtype: funtype(n;A;T),
subtract: n - m,
uncurry-rev: uncurry-rev(n;f),
uncurry-gen: uncurry-gen(n),
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
bfalse: ff,
btrue: tt,
lifting1-loc: lifting1-loc(f;loc;b),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
simple-loc-comb1: simple-loc-comb1(l,b.F[l; b];X)
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].
uiff(v \mmember{} simple-loc-comb1(l,a.lifting1-loc(f;l;a);X)(e);\mdownarrow{}\mexists{}b:B. (b \mmember{} X(e) \mwedge{} (v = (f loc(e) b))))
Date html generated:
2016_05_17-AM-09_18_11
Last ObjectModification:
2016_01_17-PM-11_15_32
Theory : classrel!lemmas
Home
Index