### 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

Home Index