Nuprl Lemma : glue-composes
∀[Info:Type]
∀es:EO+(Info)
∀[A,B,C:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀Ic:EClass(C). ∀f1:E(Ia) ─→ B. ∀f2:B ─→ C. ∀g1:E(Ib) ─→ E. ∀g2:E(Ic) ─→ E.
((g1 glues Ia ──f1─→ Ib ∧ g2 glues Ib ──λe.(f2 Ib(e))─→ Ic) ⇒ g1 o g2 glues Ia ──f2 o f1─→ Ic)
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-E: E,
compose: f o g,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
apply: f a,
lambda: λx.A[x],
function: x:A ─→ B[x],
universe: Type
Lemmas :
glues_wf,
eclass-val_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
assert_elim,
in-eclass_wf,
subtype_base_sq,
bool_wf,
bool_subtype_base,
es-E-interface_wf,
es-interface-subtype_rel2,
top_wf,
eclass_wf,
es-le_wf,
Q-R-glues-composes,
glues-property
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B,C:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}Ic:EClass(C). \mforall{}f1:E(Ia) {}\mrightarrow{} B. \mforall{}f2:B {}\mrightarrow{} C. \mforall{}g1:E(Ib) {}\mrightarrow{} E.
\mforall{}g2:E(Ic) {}\mrightarrow{} E.
((g1 glues Ia {}{}f1{}\mrightarrow{} Ib \mwedge{} g2 glues Ib {}{}\mlambda{}e.(f2 Ib(e)){}\mrightarrow{} Ic)
{}\mRightarrow{} g1 o g2 glues Ia {}{}f2 o f1{}\mrightarrow{} Ic)
Date html generated:
2015_07_21-PM-04_15_30
Last ObjectModification:
2015_01_27-PM-05_46_52
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