Nuprl Lemma : glued-composes-simple
∀[Info:Type]
∀es:EO+(Info)
∀[A,B:Type].
∀Ia:EClass(A). ∀Ib,Ic:EClass(B). ∀f1:E(Ia) ⟶ B.
((glued(es;B;f1;Ia;Ib) ∧ glued(es;B;λe.Ib(e);Ib;Ic)) ⇒ glued(es;B;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),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
lambda: λx.A[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
so_apply: x[s1;s2],
subtype_rel: A ⊆r B,
so_lambda: λ2x y.t[x; y],
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
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),
prop: ℙ,
pi1: fst(t),
hd: hd(l),
bag-only: only(bs),
eclass-val: X(e),
cand: A c∧ B,
and: P ∧ Q,
implies: P ⇒ Q,
compose: f o g
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib,Ic:EClass(B). \mforall{}f1:E(Ia) {}\mrightarrow{} B.
((glued(es;B;f1;Ia;Ib) \mwedge{} glued(es;B;\mlambda{}e.Ib(e);Ib;Ic)) {}\mRightarrow{} glued(es;B;f1;Ia;Ic))
Date html generated:
2016_05_17-AM-08_02_20
Last ObjectModification:
2015_12_28-PM-11_19_00
Theory : event-ordering
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