Nuprl Lemma : fpf-join-dom2
∀[A:Type]. ∀eq:EqDecider(A). ∀f,g:a:A fp-> Top. ∀x:A.  (↑x ∈ dom(f ⊕ g) 
⇐⇒ (↑x ∈ dom(f)) ∨ (↑x ∈ dom(g)))
Proof
Definitions occuring in Statement : 
fpf-join: f ⊕ g
, 
fpf-dom: x ∈ dom(f)
, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
assert: ↑b
, 
uall: ∀[x:A]. B[x]
, 
top: Top
, 
all: ∀x:A. B[x]
, 
iff: P 
⇐⇒ Q
, 
or: P ∨ Q
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
fpf-join-dom, 
top_wf, 
fpf_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
cut, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
because_Cache, 
sqequalRule, 
lambdaEquality, 
hypothesis, 
hypothesisEquality, 
dependent_functionElimination, 
universeEquality
Latex:
\mforall{}[A:Type]
    \mforall{}eq:EqDecider(A).  \mforall{}f,g:a:A  fp->  Top.  \mforall{}x:A.    (\muparrow{}x  \mmember{}  dom(f  \moplus{}  g)  \mLeftarrow{}{}\mRightarrow{}  (\muparrow{}x  \mmember{}  dom(f))  \mvee{}  (\muparrow{}x  \mmember{}  dom(g)))
Date html generated:
2018_05_21-PM-09_21_28
Last ObjectModification:
2018_02_09-AM-10_18_18
Theory : finite!partial!functions
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