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Step * 1 of Lemma fpf-join-dom-decl


1. f : x:Id fp-> Type@i'
2. g : x:Id fp-> Type@i'
3. x : Id@i
⊢ ↑x ∈ dom(f ⊕ g) ⇐⇒ (↑x ∈ dom(f)) ∨ (↑x ∈ dom(g))
BY
{ (RWO "fpf-join-dom" 0 THEN Auto) }

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Latex:



1.  f  :  x:Id  fp->  Type@i'
2.  g  :  x:Id  fp->  Type@i'
3.  x  :  Id@i
\mvdash{}  \muparrow{}x  \mmember{}  dom(f  \moplus{}  g)  \mLeftarrow{}{}\mRightarrow{}  (\muparrow{}x  \mmember{}  dom(f))  \mvee{}  (\muparrow{}x  \mmember{}  dom(g))


By

(RWO  "fpf-join-dom"  0  THEN  Auto)

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