Nuprl Lemma : RankEx4-induction
∀[P:RankEx4() ─→ ℙ]
((∀foo:ℤ + RankEx4(). (case foo of inl(u) => True | inr(u1) => P[u1] ⇒ P[RankEx4_Foo(foo)])) ⇒ {∀v:RankEx4(). P[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[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
true: True,
function: x:A ─→ B[x],
decide: case b of inl(x) => s[x] | inr(y) => t[y],
union: left + right,
int: ℤ
Lemmas :
uniform-comp-nat-induction,
all_wf,
isect_wf,
le_wf,
RankEx4_size_wf,
nat_wf,
less_than_wf,
RankEx4-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
subtract_wf,
decidable__le,
false_wf,
not-le-2,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-swap,
add-commutes,
add_functionality_wrt_le,
le-add-cancel,
subtract-is-less,
lelt_wf,
decidable__lt,
less-iff-le,
add-zero,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
uall_wf,
int_seg_wf,
le_weakening,
RankEx4_wf,
true_wf,
RankEx4_Foo_wf
\mforall{}[P:RankEx4() {}\mrightarrow{} \mBbbP{}]
((\mforall{}foo:\mBbbZ{} + RankEx4(). (case foo of inl(u) => True | inr(u1) => P[u1] {}\mRightarrow{} P[RankEx4\_Foo(foo)]))
{}\mRightarrow{} \{\mforall{}v:RankEx4(). P[v]\})
Date html generated:
2015_07_17-AM-07_51_14
Last ObjectModification:
2015_01_27-AM-09_36_14
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