Nuprl Lemma : rec-comb_wf2
∀[Info:Type]. ∀[n,m:ℕ]. ∀[A:{m..n-} ─→ Type]. ∀[X:i:{m..n-} ─→ EClass(A i)]. ∀[T:Type]. ∀[f:Id
─→ (i:{m..n-} ─→ bag(A i))
─→ bag(T)
─→ bag(T)].
∀[init:Id ─→ bag(T)].
(rec-comb(X;f;init) ∈ EClass(T))
Proof
Definitions occuring in Statement :
rec-comb: rec-comb(X;f;init),
eclass: EClass(A[eo; e]),
Id: Id,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ─→ B[x],
universe: Type,
bag: bag(T)
Lemmas :
bag_wf,
Id_wf,
int_seg_wf,
eclass_wf,
es-E_wf,
event-ordering+_subtype,
event-ordering+_wf,
nat_wf,
top_wf,
es-causl-swellfnd,
nat_properties,
less_than_transitivity1,
less_than_irreflexivity,
ge_wf,
less_than_wf,
int_seg_subtype-nat,
decidable__le,
subtract_wf,
false_wf,
not-ge-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,
decidable__equal_int,
subtype_rel-int_seg,
le_weakening,
int_seg_properties,
le_wf,
zero-le-nat,
lelt_wf,
es-causl_wf,
es-local-pred_wf2,
es-locl_wf,
lt_int_wf,
bag-size_wf,
es-causl_weakening,
equal_wf,
decidable__lt,
not-equal-2,
le-add-cancel-alt,
not-le-2,
sq_stable__le,
add-mul-special,
zero-mul
Latex:
\mforall{}[Info:Type]. \mforall{}[n,m:\mBbbN{}]. \mforall{}[A:\{m..n\msupminus{}\} {}\mrightarrow{} Type]. \mforall{}[X:i:\{m..n\msupminus{}\} {}\mrightarrow{} EClass(A i)]. \mforall{}[T:Type].
\mforall{}[f:Id {}\mrightarrow{} (i:\{m..n\msupminus{}\} {}\mrightarrow{} bag(A i)) {}\mrightarrow{} bag(T) {}\mrightarrow{} bag(T)]. \mforall{}[init:Id {}\mrightarrow{} bag(T)].
(rec-comb(X;f;init) \mmember{} EClass(T))
Date html generated:
2015_07_21-PM-02_49_21
Last ObjectModification:
2015_01_27-PM-07_41_30
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