Nuprl Lemma : Q-R-glues-composes
∀[Info:Type]
∀es:EO+(Info)
∀[Qa,Rb,Sc:E ─→ E ─→ ℙ]. ∀[A,B,C:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀Ic:EClass(C). ∀f1:E(Ia) ─→ B. ∀f2:B ─→ C. ∀g1:E(Ib) ─→ E(Ia). ∀g2:E(Ic) ─→ E(Ib).
((g1 glues Ia:Qa ──f1─→ Ib:Rb ∧ g2 glues Ib:Rb ──λe.(f2 Ib(e))─→ Ic:Sc)
⇒ g1 o g2 glues Ia:Qa ──f2 o f1─→ Ic:Sc)
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f─→ Ib:Rb,
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],
prop: ℙ,
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 :
weak-antecedent-surjections-compose,
event-ordering+_subtype,
assert_wf,
in-eclass_wf,
es-interface-subtype_rel2,
es-E_wf,
event-ordering+_wf,
top_wf,
Q-R-pre-preserving-compose,
subtype_rel_dep_function,
es-E-interface_wf,
set_wf,
strong-subtype-self,
inject-composes,
equal_wf
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[Qa,Rb,Sc:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \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(Ia).
\mforall{}g2:E(Ic) {}\mrightarrow{} E(Ib).
((g1 glues Ia:Qa {}{}f1{}\mrightarrow{} Ib:Rb \mwedge{} g2 glues Ib:Rb {}{}\mlambda{}e.(f2 Ib(e)){}\mrightarrow{} Ic:Sc)
{}\mRightarrow{} g1 o g2 glues Ia:Qa {}{}f2 o f1{}\mrightarrow{} Ic:Sc)
Date html generated:
2015_07_21-PM-04_09_11
Last ObjectModification:
2015_01_27-PM-05_45_46
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