Nuprl Lemma : glued-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.
((glued(es;B;f1;Ia;Ib) ∧ glued(es;C;λe.(f2 Ib(e));Ib;Ic)) ⇒ glued(es;C;f2 o f1;Ia;Ic))
Proof
Definitions occuring in Statement :
glued: glued(es;B;f;Ia;Ib),
es-E-interface: E(X),
eclass-val: X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
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 :
glued_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,
glues-property,
compose_wf,
glues_wf,
glue-composes
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.
((glued(es;B;f1;Ia;Ib) \mwedge{} glued(es;C;\mlambda{}e.(f2 Ib(e));Ib;Ic)) {}\mRightarrow{} glued(es;C;f2 o f1;Ia;Ic))
Date html generated:
2015_07_21-PM-04_15_43
Last ObjectModification:
2015_01_27-PM-05_46_35
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