Nuprl Lemma : fpf-union-join-ap
∀[f,g,eq,x,R:Top].  (fpf-union-join(eq;R;f;g)(x) ~ fpf-union(f;g;eq;R;x))
Proof
Definitions occuring in Statement : 
fpf-union-join: fpf-union-join(eq;R;f;g)
, 
fpf-union: fpf-union(f;g;eq;R;x)
, 
fpf-ap: f(x)
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
sqequal: s ~ t
Definitions unfolded in proof : 
fpf-union-join: fpf-union-join(eq;R;f;g)
, 
fpf-ap: f(x)
, 
pi2: snd(t)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
Lemmas referenced : 
top_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
sqequalRule, 
cut, 
lemma_by_obid, 
hypothesis, 
because_Cache, 
isect_memberFormation, 
introduction, 
sqequalAxiom, 
sqequalHypSubstitution, 
isect_memberEquality, 
isectElimination, 
thin, 
hypothesisEquality
Latex:
\mforall{}[f,g,eq,x,R:Top].    (fpf-union-join(eq;R;f;g)(x)  \msim{}  fpf-union(f;g;eq;R;x))
Date html generated:
2018_05_21-PM-09_23_28
Last ObjectModification:
2018_02_09-AM-10_19_20
Theory : finite!partial!functions
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