Nuprl Lemma : mFOL-induction
∀[P:mFOL() ─→ ℙ]
  ((∀name:Atom. ∀vars:ℤ List.  P[name(vars)])
  
⇒ (∀knd:Atom. ∀left,right:mFOL().  (P[left] 
⇒ P[right] 
⇒ P[mFOconnect(knd;left;right)]))
  
⇒ (∀isall:𝔹. ∀var:ℤ. ∀body:mFOL().  (P[body] 
⇒ P[mFOquant(isall;var;body)]))
  
⇒ {∀v:mFOL(). P[v]})
Proof
Definitions occuring in Statement : 
mFOquant: mFOquant(isall;var;body)
, 
mFOconnect: mFOconnect(knd;left;right)
, 
mFOatomic: name(vars)
, 
mFOL: mFOL()
, 
list: T List
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
guard: {T}
, 
so_apply: x[s]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
function: x:A ─→ B[x]
, 
int: ℤ
, 
atom: Atom
Lemmas : 
uniform-comp-nat-induction, 
all_wf, 
mFOL_wf, 
isect_wf, 
le_wf, 
mFOL_size_wf, 
nat_wf, 
less_than_wf, 
mFOL-ext, 
eq_atom_wf, 
bool_wf, 
eqtt_to_assert, 
assert_of_eq_atom, 
subtype_base_sq, 
atom_subtype_base, 
eqff_to_assert, 
equal_wf, 
bool_cases_sqequal, 
bool_subtype_base, 
assert-bnot, 
neg_assert_of_eq_atom, 
subtract_wf, 
decidable__le, 
false_wf, 
not-le-2, 
less-iff-le, 
condition-implies-le, 
minus-one-mul, 
zero-add, 
minus-add, 
minus-minus, 
add-associates, 
add-swap, 
add-commutes, 
add_functionality_wrt_le, 
add-zero, 
le-add-cancel, 
subtract-is-less, 
lelt_wf, 
decidable__lt, 
uall_wf, 
int_seg_wf, 
le_weakening, 
mFOquant_wf, 
mFOconnect_wf, 
list_wf, 
mFOatomic_wf
\mforall{}[P:mFOL()  {}\mrightarrow{}  \mBbbP{}]
    ((\mforall{}name:Atom.  \mforall{}vars:\mBbbZ{}  List.    P[name(vars)])
    {}\mRightarrow{}  (\mforall{}knd:Atom.  \mforall{}left,right:mFOL().    (P[left]  {}\mRightarrow{}  P[right]  {}\mRightarrow{}  P[mFOconnect(knd;left;right)]))
    {}\mRightarrow{}  (\mforall{}isall:\mBbbB{}.  \mforall{}var:\mBbbZ{}.  \mforall{}body:mFOL().    (P[body]  {}\mRightarrow{}  P[mFOquant(isall;var;body)]))
    {}\mRightarrow{}  \{\mforall{}v:mFOL().  P[v]\})
Date html generated:
2015_07_17-AM-07_53_49
Last ObjectModification:
2015_01_27-AM-10_07_04
Home
Index