Nuprl Lemma : glues-iff
∀[Info:Type]
∀es:EO+(Info)
∀[A,B:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀f:E(Ia) ─→ B. ∀g:E(Ib) ─→ E(Ia).
(g glues Ia ──f─→ Ib
⇐⇒ {Bij(E(Ib);E(Ia);g)
∧ (∀e:E(Ib). g e c≤ e)
∧ (∀e,e':E(Ib). (g e ≤loc g e' ⇒ e ≤loc e' ))
∧ (∀e:E(Ib). ((f (g e)) = Ib(e) ∈ B))})
Proof
Definitions occuring in Statement :
glues: g glues Ia ──f─→ Ib,
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-causle: e c≤ e',
es-le: e ≤loc e' ,
biject: Bij(A;B;f),
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
glues_wf,
subtype_rel_dep_function,
es-E-interface_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
top_wf,
biject_wf,
all_wf,
es-causle_wf,
es-le_wf,
equal_wf,
eclass-val_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
eclass_wf,
interface_predicate_set_lemma,
equal_functionality_wrt_subtype_rel2,
assert_wf,
and_wf,
es-E-interface-property
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f:E(Ia) {}\mrightarrow{} B. \mforall{}g:E(Ib) {}\mrightarrow{} E(Ia).
(g glues Ia {}{}f{}\mrightarrow{} Ib
\mLeftarrow{}{}\mRightarrow{} \{Bij(E(Ib);E(Ia);g)
\mwedge{} (\mforall{}e:E(Ib). g e c\mleq{} e)
\mwedge{} (\mforall{}e,e':E(Ib). (g e \mleq{}loc g e' {}\mRightarrow{} e \mleq{}loc e' ))
\mwedge{} (\mforall{}e:E(Ib). ((f (g e)) = Ib(e)))\})
Date html generated:
2015_07_21-PM-04_14_13
Last ObjectModification:
2015_01_27-PM-05_50_12
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