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
Lemmas :
RankEx4_ind_wf,
true_wf,
RankEx4_wf,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
decide_wf,
top_wf,
subtype_rel_sum
\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:
2015_07_17-AM-07_51_23
Last ObjectModification:
2015_01_28-PM-02_30_28
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