Nuprl Lemma : modify-combinator2_wf
∀[n:ℕ]. ∀[A:ℕn ─→ Type]. ∀[m:ℕ].
∀[B:ℕm ─→ Type]. ∀[T:Type]. ∀[f:(i:ℕn ─→ (A i + Top)) ─→ (i:ℕm ─→ (B i + Top)) ─→ T].
(modify-combinator2(f) ∈ (i:ℕn ─→ (A i + Top))
─→ (i:ℕm - 1 ─→ if (i =z 0) then one_or_both(B 0;B 1) + Top else B (i + 1) + Top fi )
─→ T)
supposing 1 < m
Proof
Definitions occuring in Statement :
modify-combinator2: modify-combinator2(f),
int_seg: {i..j-},
nat: ℕ,
ifthenelse: if b then t else f fi ,
eq_int: (i =z j),
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
top: Top,
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
union: left + right,
subtract: n - m,
add: n + m,
natural_number: $n,
universe: Type,
one_or_both: one_or_both(A;B)
Lemmas :
eq_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_int,
false_wf,
decidable__lt,
subtract_wf,
less-iff-le,
condition-implies-le,
minus-add,
minus-minus,
minus-one-mul,
zero-add,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-swap,
le-add-cancel,
lelt_wf,
one_or_both_wf,
top_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_int,
oob-hasleft_wf,
oob-getleft_wf,
int_subtype_base,
subtype_rel_self,
assert_wf,
not-equal-2,
oob-hasright_wf,
oob-getright_wf,
decidable__le,
not-le-2,
sq_stable__le,
add-zero,
minus-zero,
le-add-cancel-alt,
subtype_rel-equal,
le_antisymmetry_iff,
le-add-cancel2,
int_seg_wf,
less_than_wf,
nat_wf
\mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[m:\mBbbN{}].
\mforall{}[B:\mBbbN{}m {}\mrightarrow{} Type]. \mforall{}[T:Type]. \mforall{}[f:(i:\mBbbN{}n {}\mrightarrow{} (A i + Top)) {}\mrightarrow{} (i:\mBbbN{}m {}\mrightarrow{} (B i + Top)) {}\mrightarrow{} T].
(modify-combinator2(f) \mmember{} (i:\mBbbN{}n {}\mrightarrow{} (A i + Top))
{}\mrightarrow{} (i:\mBbbN{}m - 1 {}\mrightarrow{} if (i =\msubz{} 0) then one\_or\_both(B 0;B 1) + Top else B (i + 1) + Top fi )
{}\mrightarrow{} T)
supposing 1 < m
Date html generated:
2015_07_17-AM-08_59_37
Last ObjectModification:
2015_01_27-PM-01_05_45
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