Nuprl Lemma : embedding-preserves-local-relation
∀[Info:Type]. ∀[R:Id ⟶ Id ⟶ Info List+ ⟶ Info List+ ⟶ ℙ]. ∀[eo1:EO+(Info)].
∀eo2:EO+(Info). ∀f:E ⟶ E.
(es-local-embedding(Info;eo1;eo2;f)
⇒ (∀[e1,e2:E].
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo1;e1;e2)
⇐⇒ es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo2;f e1;f e2))))
Proof
Definitions occuring in Statement :
es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2),
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
event-ordering+: EO+(Info),
es-E: E,
Id: Id,
listp: A List+,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2;s3;s4],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
es-local-relation: es-local-relation(i,j,L1,L2.R[i; j; L1; L2];es;e1;e2),
so_apply: x[s1;s2;s3;s4],
listp: A List+,
member: t ∈ T,
top: Top,
es-le-before: ≤loc(e),
subtype_rel: A ⊆r B,
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
true: True,
prop: ℙ,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
false: False,
uiff: uiff(P;Q),
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
rev_implies: P ⇐ Q,
es-local-embedding: es-local-embedding(Info;eo1;eo2;f)
Latex:
\mforall{}[Info:Type]. \mforall{}[R:Id {}\mrightarrow{} Id {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} Info List\msupplus{} {}\mrightarrow{} \mBbbP{}]. \mforall{}[eo1:EO+(Info)].
\mforall{}eo2:EO+(Info). \mforall{}f:E {}\mrightarrow{} E.
(es-local-embedding(Info;eo1;eo2;f)
{}\mRightarrow{} (\mforall{}[e1,e2:E].
(es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo1;e1;e2)
\mLeftarrow{}{}\mRightarrow{} es-local-relation(i,j,L1,L2.R[i;j;L1;L2];eo2;f e1;f e2))))
Date html generated:
2016_05_16-PM-01_23_30
Last ObjectModification:
2016_01_17-PM-07_58_30
Theory : event-ordering
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