Nuprl Lemma : RankEx4-definition
∀[A:Type]. ∀[R:A ⟶ RankEx4() ⟶ ℙ].
  ((∀foo:ℤ + RankEx4(). (case foo of inl(u) => True | inr(u1) => {x:A| R[x;u1]}  
⇒ {x:A| R[x;RankEx4_Foo(foo)]} ))
  
⇒ {∀v:RankEx4(). {x:A| R[x;v]} })
Proof
Definitions occuring in Statement : 
RankEx4_Foo: RankEx4_Foo(foo)
, 
RankEx4: RankEx4()
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
guard: {T}
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
true: True
, 
set: {x:A| B[x]} 
, 
function: x:A ⟶ B[x]
, 
decide: case b of inl(x) => s[x] | inr(y) => t[y]
, 
union: left + right
, 
int: ℤ
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
so_lambda: λ2x.t[x]
, 
member: t ∈ T
, 
so_apply: x[s1;s2]
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
prop: ℙ
Lemmas referenced : 
RankEx4-induction, 
set_wf, 
RankEx4_wf, 
all_wf, 
true_wf, 
RankEx4_Foo_wf
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
lambdaFormation, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
sqequalRule, 
lambdaEquality, 
hypothesisEquality, 
applyEquality, 
because_Cache, 
independent_functionElimination, 
unionEquality, 
intEquality, 
functionEquality, 
decideEquality, 
universeEquality, 
cumulativity
Latex:
\mforall{}[A:Type].  \mforall{}[R:A  {}\mrightarrow{}  RankEx4()  {}\mrightarrow{}  \mBbbP{}].
    ((\mforall{}foo:\mBbbZ{}  +  RankEx4()
            (case  foo  of  inl(u)  =>  True  |  inr(u1)  =>  \{x:A|  R[x;u1]\}    {}\mRightarrow{}  \{x:A|  R[x;RankEx4\_Foo(foo)]\}  ))
    {}\mRightarrow{}  \{\mforall{}v:RankEx4().  \{x:A|  R[x;v]\}  \})
Date html generated:
2016_05_16-AM-09_04_41
Last ObjectModification:
2015_12_28-PM-06_50_43
Theory : C-semantics
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