Nuprl Lemma : rec-comb-es-sv
∀[Info,B:Type]. ∀[n:ℕ]. ∀[A:ℕn ⟶ Type]. ∀[Xs:k:ℕn ⟶ EClass(A k)]. ∀[F:Id ⟶ (k:ℕn ⟶ bag(A k)) ⟶ bag(B) ⟶ bag(B)].
∀[init:Id ⟶ bag(B)]. ∀[es:EO+(Info)].
(es-sv-class(es;rec-comb(Xs;F;init))) supposing
((∀bs:k:ℕn ⟶ bag(A k). ∀l:Id. ∀b:bag(B). ((∀k:ℕn. (#(bs k) ≤ 1)) ⇒ (#(b) ≤ 1) ⇒ (#(F l bs b) ≤ 1))) and
(∀k:ℕn. es-sv-class(es;Xs k)) and
(∀l:Id. (#(init l) ≤ 1)))
Proof
Definitions occuring in Statement :
rec-comb: rec-comb(X;f;init),
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
Id: Id,
int_seg: {i..j-},
nat: ℕ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type,
bag-size: #(bs),
bag: bag(T)
Definitions unfolded in proof :
es-sv-class: es-sv-class(es;X),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
strongwellfounded: SWellFounded(R[x; y]),
exists: ∃x:A. B[x],
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
guard: {T},
le: A ≤ B,
less_than': less_than'(a;b),
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
rec-comb: rec-comb(X;f;init),
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uiff: uiff(P;Q),
so_lambda: λ2x.t[x],
so_apply: x[s],
es-locl: (e <loc e')
Latex:
\mforall{}[Info,B:Type]. \mforall{}[n:\mBbbN{}]. \mforall{}[A:\mBbbN{}n {}\mrightarrow{} Type]. \mforall{}[Xs:k:\mBbbN{}n {}\mrightarrow{} EClass(A k)]. \mforall{}[F:Id
{}\mrightarrow{} (k:\mBbbN{}n {}\mrightarrow{} bag(A k))
{}\mrightarrow{} bag(B)
{}\mrightarrow{} bag(B)].
\mforall{}[init:Id {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)].
(es-sv-class(es;rec-comb(Xs;F;init))) supposing
((\mforall{}bs:k:\mBbbN{}n {}\mrightarrow{} bag(A k). \mforall{}l:Id. \mforall{}b:bag(B).
((\mforall{}k:\mBbbN{}n. (\#(bs k) \mleq{} 1)) {}\mRightarrow{} (\#(b) \mleq{} 1) {}\mRightarrow{} (\#(F l bs b) \mleq{} 1))) and
(\mforall{}k:\mBbbN{}n. es-sv-class(es;Xs k)) and
(\mforall{}l:Id. (\#(init l) \mleq{} 1)))
Date html generated:
2016_05_17-AM-09_28_26
Last ObjectModification:
2016_01_17-PM-11_10_09
Theory : classrel!lemmas
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