Nuprl Lemma : pi_term-induction
∀[P:pi_term() ─→ ℙ]
(P[pizero()]
⇒ (∀pre:pi_prefix(). ∀body:pi_term(). (P[body] ⇒ P[picomm(pre;body)]))
⇒ (∀left,right:pi_term(). (P[left] ⇒ P[right] ⇒ P[pioption(left;right)]))
⇒ (∀left,right:pi_term(). (P[left] ⇒ P[right] ⇒ P[pipar(left;right)]))
⇒ (∀body:pi_term(). (P[body] ⇒ P[pirep(body)]))
⇒ (∀name:Name. ∀body:pi_term(). (P[body] ⇒ P[pinew(name;body)]))
⇒ {∀v:pi_term(). P[v]})
Proof
Definitions occuring in Statement :
pinew: pinew(name;body),
pirep: pirep(body),
pipar: pipar(left;right),
pioption: pioption(left;right),
picomm: picomm(pre;body),
pizero: pizero(),
pi_term: pi_term(),
pi_prefix: pi_prefix(),
name: Name,
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]
Lemmas :
uniform-comp-nat-induction,
all_wf,
isect_wf,
le_wf,
pi_term_size_wf,
nat_wf,
less_than_wf,
pi_term-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
unit_wf2,
unit_subtype_base,
it_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
decidable__lt,
false_wf,
add_functionality_wrt_le,
add-swap,
add-commutes,
le-add-cancel,
subtract_wf,
decidable__le,
not-le-2,
less-iff-le,
condition-implies-le,
minus-one-mul,
zero-add,
minus-add,
minus-minus,
add-associates,
add-zero,
subtract-is-less,
lelt_wf,
uall_wf,
int_seg_wf,
le_weakening,
name_wf,
pinew_wf,
pirep_wf,
pipar_wf,
pi_term_wf,
pioption_wf,
pi_prefix_wf,
picomm_wf,
pizero_wf
Latex:
\mforall{}[P:pi\_term() {}\mrightarrow{} \mBbbP{}]
(P[pizero()]
{}\mRightarrow{} (\mforall{}pre:pi\_prefix(). \mforall{}body:pi\_term(). (P[body] {}\mRightarrow{} P[picomm(pre;body)]))
{}\mRightarrow{} (\mforall{}left,right:pi\_term(). (P[left] {}\mRightarrow{} P[right] {}\mRightarrow{} P[pioption(left;right)]))
{}\mRightarrow{} (\mforall{}left,right:pi\_term(). (P[left] {}\mRightarrow{} P[right] {}\mRightarrow{} P[pipar(left;right)]))
{}\mRightarrow{} (\mforall{}body:pi\_term(). (P[body] {}\mRightarrow{} P[pirep(body)]))
{}\mRightarrow{} (\mforall{}name:Name. \mforall{}body:pi\_term(). (P[body] {}\mRightarrow{} P[pinew(name;body)]))
{}\mRightarrow{} \{\mforall{}v:pi\_term(). P[v]\})
Date html generated:
2015_07_23-AM-11_32_43
Last ObjectModification:
2015_01_29-AM-00_55_04
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