Nuprl Lemma : weak-antecedent-functions-compose
∀es:EO
∀[P,Q,R:E ─→ ℙ].
∀f:{e:E| P e} ─→ {e:E| Q e} . ∀g:{e:E| Q e} ─→ {e:E| R e} . ((Q ←==f== P ∧ R ←==g== Q) ⇒ R ←==g o f== P)
Proof
Definitions occuring in Statement :
weak-antecedent-function: Q ←==f== 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 :
set_wf,
weak-antecedent-function_wf,
subtype_rel_dep_function,
es-E_wf,
event_ordering_wf,
es-causle_transitivity
\mforall{}es:EO
\mforall{}[P,Q,R:E {}\mrightarrow{} \mBbbP{}].
\mforall{}f:\{e:E| P e\} {}\mrightarrow{} \{e:E| Q e\} . \mforall{}g:\{e:E| Q e\} {}\mrightarrow{} \{e:E| R e\} .
((Q \mleftarrow{}==f== P \mwedge{} R \mleftarrow{}==g== Q) {}\mRightarrow{} R \mleftarrow{}==g o f== P)
Date html generated:
2015_07_17-AM-09_02_00
Last ObjectModification:
2015_01_27-PM-00_55_03
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