Nuprl Lemma : simple-loc-comb2-classrel
∀[Info,A,B,C:Type]. ∀[f:Id ⟶ A ⟶ B ⟶ C]. ∀[X:EClass(A)]. ∀[Y:EClass(B)]. ∀[es:EO+(Info)]. ∀[e:E]. ∀[v:C].
uiff(v ∈ simple-loc-comb2(l,a,b.lifting2-loc(f;l;a;b);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 :
lifting2-loc: lifting2-loc(f;loc;abag;bbag),
simple-loc-comb2: simple-loc-comb2(l,a,b.F[l; a; b];X;Y),
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: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
so_lambda: λ2x.t[x],
prop: ℙ,
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
uimplies: b supposing a,
squash: ↓T,
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],
subtract: n - m,
less_than: a < b,
true: True,
funtype: funtype(n;A;T),
eq_int: (i =z j),
ifthenelse: if b then t else f fi ,
bfalse: ff,
lifting2-loc: lifting2-loc(f;loc;abag;bbag),
uncurry-rev: uncurry-rev(n;f),
uncurry-gen: uncurry-gen(n),
btrue: tt,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
cand: A c∧ B,
simple-loc-comb2: simple-loc-comb2(l,a,b.F[l; a; b];X;Y)
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].
uiff(v \mmember{} simple-loc-comb2(l,a,b.lifting2-loc(f;l;a;b);X;Y)(e);\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_35
Last ObjectModification:
2016_01_17-PM-11_16_26
Theory : classrel!lemmas
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