Nuprl Lemma : Accum-class-invariant
∀[Info,B,A:Type].
∀P:B ⟶ ℙ. ∀f:A ⟶ B ⟶ B. ∀init:Id ⟶ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.
((∀s:B. SqStable(P[s]))
⇒ (∀a:A. ∀e':E. (e' ≤loc e ⇒ a ∈ X(e') ⇒ (∀s:B. (P[s] ⇒ P[f a s]))))
⇒ (∀v:B. (v ↓∈ init loc(e) ⇒ P[v]))
⇒ v ∈ Accum-class(f;init;X)(e)
⇒ P[v])
Proof
Definitions occuring in Statement :
Accum-class: Accum-class(f;init;X),
classrel: v ∈ X(e),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-le: e ≤loc e' ,
es-loc: loc(e),
es-E: E,
Id: Id,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
all: ∀x:A. B[x],
implies: P ⇒ Q,
apply: f a,
function: x:A ⟶ B[x],
universe: Type,
bag-member: x ↓∈ bs,
bag: bag(T)
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
squash: ↓T,
sq_stable: SqStable(P),
exists: ∃x:A. B[x],
guard: {T},
subtype_rel: A ⊆r B,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Latex:
\mforall{}[Info,B,A:Type].
\mforall{}P:B {}\mrightarrow{} \mBbbP{}. \mforall{}f:A {}\mrightarrow{} B {}\mrightarrow{} B. \mforall{}init:Id {}\mrightarrow{} bag(B). \mforall{}X:EClass(A). \mforall{}es:EO+(Info). \mforall{}e:E. \mforall{}v:B.
((\mforall{}s:B. SqStable(P[s]))
{}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. (e' \mleq{}loc e {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} (\mforall{}s:B. (P[s] {}\mRightarrow{} P[f a s]))))
{}\mRightarrow{} (\mforall{}v:B. (v \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[v]))
{}\mRightarrow{} v \mmember{} Accum-class(f;init;X)(e)
{}\mRightarrow{} P[v])
Date html generated:
2016_05_17-AM-09_32_53
Last ObjectModification:
2016_01_17-PM-11_08_00
Theory : classrel!lemmas
Home
Index