Nuprl Lemma : es-local-embedding-compose
∀[Info:Type]. ∀[eo1,eo2,eo3:EO+(Info)]. ∀[f:E ⟶ E]. ∀[g:E ⟶ E].
(es-local-embedding(Info;eo1;eo2;f) ⇒ es-local-embedding(Info;eo2;eo3;g) ⇒ es-local-embedding(Info;eo1;eo3;g o f))
Proof
Definitions occuring in Statement :
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
event-ordering+: EO+(Info),
es-E: E,
compose: f o g,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
es-local-embedding: es-local-embedding(Info;eo1;eo2;f),
compose: f o g,
all: ∀x:A. B[x],
and: P ∧ Q,
cand: A c∧ B,
prop: ℙ,
subtype_rel: A ⊆r B
Latex:
\mforall{}[Info:Type]. \mforall{}[eo1,eo2,eo3:EO+(Info)]. \mforall{}[f:E {}\mrightarrow{} E]. \mforall{}[g:E {}\mrightarrow{} E].
(es-local-embedding(Info;eo1;eo2;f)
{}\mRightarrow{} es-local-embedding(Info;eo2;eo3;g)
{}\mRightarrow{} es-local-embedding(Info;eo1;eo3;g o f))
Date html generated:
2016_05_16-PM-01_22_00
Last ObjectModification:
2015_12_29-PM-01_59_45
Theory : event-ordering
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