Nuprl Lemma : simple-comb-es-sv
∀[Info,B:Type]. ∀[n:ℕ]. ∀[A:ℕn ⟶ Type]. ∀[Xs:k:ℕn ⟶ EClass(A k)]. ∀[F:(k:ℕn ⟶ bag(A k)) ⟶ bag(B)]. ∀[es:EO+(Info)].
(es-sv-class(es;simple-comb(F;Xs))) supposing
((∀bs:k:ℕn ⟶ bag(A k). ((∀k:ℕn. (#(bs k) ≤ 1)) ⇒ (#(F bs) ≤ 1))) and
(∀k:ℕn. es-sv-class(es;Xs k)))
Proof
Definitions occuring in Statement :
simple-comb: simple-comb(F;Xs),
es-sv-class: es-sv-class(es;X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
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 :
simple-comb: simple-comb(F;Xs),
es-sv-class: es-sv-class(es;X),
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
nat: ℕ,
implies: P ⇒ Q,
guard: {T},
eclass: EClass(A[eo; e]),
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False
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:(k:\mBbbN{}n {}\mrightarrow{} bag(A k)) {}\mrightarrow{} bag(B)]. \mforall{}[es:EO+(Info)].
(es-sv-class(es;simple-comb(F;Xs))) supposing
((\mforall{}bs:k:\mBbbN{}n {}\mrightarrow{} bag(A k). ((\mforall{}k:\mBbbN{}n. (\#(bs k) \mleq{} 1)) {}\mRightarrow{} (\#(F bs) \mleq{} 1))) and
(\mforall{}k:\mBbbN{}n. es-sv-class(es;Xs k)))
Date html generated:
2016_05_17-AM-09_29_34
Last ObjectModification:
2015_12_29-PM-04_01_55
Theory : classrel!lemmas
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