Nuprl Lemma : locl-pre-preserving-compose
∀es:EO
∀[P,Q:E ─→ ℙ].
∀f1:{e:E| P e} ─→ {e:E| Q e} . ∀f2:{e:E| Q e} ─→ E.
((f1 is locl-pre-preserving on P ∧ f2 is locl-pre-preserving on Q) ⇒ f2 o f1 is locl-pre-preserving on P)
Proof
Definitions occuring in Statement :
locl-pre-preserving: f is locl-pre-preserving on P,
es-E: E,
event_ordering: EO,
compose: f o g,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x]
Lemmas :
locl-pre-preserving_wf,
subtype_rel_dep_function,
es-E_wf,
set_wf,
event_ordering_wf,
rel-pre-preserving-compose,
es-le_wf
\mforall{}es:EO
\mforall{}[P,Q:E {}\mrightarrow{} \mBbbP{}].
\mforall{}f1:\{e:E| P e\} {}\mrightarrow{} \{e:E| Q e\} . \mforall{}f2:\{e:E| Q e\} {}\mrightarrow{} E.
((f1 is locl-pre-preserving on P \mwedge{} f2 is locl-pre-preserving on Q)
{}\mRightarrow{} f2 o f1 is locl-pre-preserving on P)
Date html generated:
2015_07_17-AM-09_03_51
Last ObjectModification:
2015_01_27-PM-00_52_24
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