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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