Nuprl Lemma : RankEx4_ind_wf_simple
∀[A:Type]. ∀[v:RankEx4()]. ∀[Foo:foo:(ℤ + RankEx4()) ⟶ case foo of inl(u) => True | inr(u1) => A ⟶ A].
  (RankEx4_ind(v;
               RankEx4_Foo(foo)
⇒ rec1.Foo[foo;rec1])  ∈ A)
Proof
Definitions occuring in Statement : 
RankEx4_ind: RankEx4_ind, 
RankEx4: RankEx4()
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s1;s2]
, 
true: True
, 
member: t ∈ T
, 
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]
, 
member: t ∈ T
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
subtype_rel: A ⊆r B
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
true: True
, 
guard: {T}
Lemmas referenced : 
RankEx4_ind_wf, 
true_wf, 
RankEx4_wf, 
subtype_rel_dep_function, 
subtype_rel_self, 
set_wf
Rules used in proof : 
cut, 
lemma_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
sqequalRule, 
lambdaEquality, 
applyEquality, 
unionEquality, 
intEquality, 
functionEquality, 
decideEquality, 
because_Cache, 
setEquality, 
independent_isectElimination, 
lambdaFormation, 
unionElimination, 
setElimination, 
rename, 
dependent_set_memberEquality, 
natural_numberEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}[v:RankEx4()].  \mforall{}[Foo:foo:(\mBbbZ{}  +  RankEx4())
                                                                  {}\mrightarrow{}  case  foo  of  inl(u)  =>  True  |  inr(u1)  =>  A
                                                                  {}\mrightarrow{}  A].
    (RankEx4\_ind(v;
                              RankEx4\_Foo(foo){}\mRightarrow{}  rec1.Foo[foo;rec1])    \mmember{}  A)
Date html generated:
2016_05_16-AM-09_04_56
Last ObjectModification:
2015_12_28-PM-06_49_25
Theory : C-semantics
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