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
Definitions unfolded in proof :
so_apply: x[s],
so_lambda: λ2x.t[x],
prop: ℙ,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
guard: {T},
sq_type: SQType(T),
top: Top,
uimplies: b supposing a,
es-E-interface: E(X),
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
member: t ∈ T,
cand: A c∧ B,
compose: f o g,
es-interface-predicate: {I},
Q-R-glues: g glues Ia:Qa ──f⟶ Ib:Rb,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
inject: Inj(A;B;f)
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:
2016_05_17-AM-07_50_53
Last ObjectModification:
2015_12_28-PM-11_31_33
Theory : event-ordering
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