Nuprl Lemma : fpf_dom_compose_lemma
∀f,g,x,eq:Top.  (x ∈ dom(g o f) ~ x ∈ dom(f))
Proof
Definitions occuring in Statement : 
fpf-compose: g o f
, 
fpf-dom: x ∈ dom(f)
, 
top: Top
, 
all: ∀x:A. B[x]
, 
sqequal: s ~ t
Definitions unfolded in proof : 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
fpf-compose: g o f
, 
fpf-dom: x ∈ dom(f)
, 
pi1: fst(t)
Lemmas referenced : 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
lambdaFormation, 
cut, 
hypothesis, 
lemma_by_obid, 
sqequalRule
Latex:
\mforall{}f,g,x,eq:Top.    (x  \mmember{}  dom(g  o  f)  \msim{}  x  \mmember{}  dom(f))
Date html generated:
2018_05_21-PM-09_27_37
Last ObjectModification:
2018_02_09-AM-10_23_07
Theory : finite!partial!functions
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