Nuprl Lemma : non-void-decl-join
∀[T:Type]. ∀eq:EqDecider(T). ∀d1,d2:a:T fp-> Type.  (non-void(d1) 
⇒ non-void(d2) 
⇒ non-void(d1 ⊕ d2))
Proof
Definitions occuring in Statement : 
non-void-decl: non-void(d)
, 
fpf-join: f ⊕ g
, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
universe: Type
Definitions unfolded in proof : 
non-void-decl: non-void(d)
, 
uall: ∀[x:A]. B[x]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
member: t ∈ T
, 
so_lambda: λ2x y.t[x; y]
, 
prop: ℙ
, 
so_apply: x[s1;s2]
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
subtype_rel: A ⊆r B
, 
uimplies: b supposing a
, 
top: Top
Lemmas referenced : 
fpf-all-join-decl, 
istype-universe, 
fpf-all_wf, 
subtype_rel_universe1, 
assert_wf, 
fpf-dom_wf, 
subtype-fpf2, 
top_wf, 
istype-void, 
fpf_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation_alt, 
lambdaFormation_alt, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
dependent_functionElimination, 
lambdaEquality_alt, 
inhabitedIsType, 
hypothesis, 
independent_functionElimination, 
universeIsType, 
instantiate, 
cumulativity, 
universeEquality, 
applyEquality, 
setIsType, 
because_Cache, 
independent_isectElimination, 
isect_memberEquality_alt, 
voidElimination
Latex:
\mforall{}[T:Type]
    \mforall{}eq:EqDecider(T).  \mforall{}d1,d2:a:T  fp->  Type.    (non-void(d1)  {}\mRightarrow{}  non-void(d2)  {}\mRightarrow{}  non-void(d1  \moplus{}  d2))
Date html generated:
2019_10_16-AM-11_26_23
Last ObjectModification:
2018_10_10-PM-02_05_12
Theory : finite!partial!functions
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