Nuprl Lemma : Memory-loc-class-invariant-sv1

∀[Info,B,A:Type].

  ∀P:B ⟶ ℙ. ∀f:Id ⟶ A ⟶ B ⟶ B. ∀init:Id ⟶ bag(B). ∀X:EClass(A). ∀es:EO+(Info). ∀e:E. ∀v:B.

    (single-valued-classrel(es;X;A)
    ⇒ single-valued-bag(init loc(e);B)
    ⇒ (∀v:B. (v ↓∈ init loc(e) ⇒ P[v]))
    ⇒ (∀a:A. ∀e':E. ∀s:B.
          ((e' <loc e) ⇒ a ∈ X(e') ⇒ s ∈ Memory-loc-class(f;init;X)(e') ⇒ P[s] ⇒ P[f loc(e') a s]))
    ⇒ v ∈ Memory-loc-class(f;init;X)(e)
    ⇒ P[v])

Proof

Definitions occuring in Statement : Memory-loc-class: Memory-loc-class(f;init;X), single-valued-classrel: single-valued-classrel(es;X;T), classrel: v ∈ X(e), eclass: EClass(A[eo; e]), event-ordering+: EO+(Info), es-locl: (e <loc e'), es-loc: loc(e), es-E: E, Id: Id, 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, single-valued-bag: single-valued-bag(b;T), 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, uiff: uiff(P;Q), and: P ∧ Q, uimplies: b supposing a, subtype_rel: A ⊆r B, es-locl: (e <loc e'), prop: ℙ, so_lambda: λ₂x y.t[x; y], so_apply: x[s1;s2], so_apply: x[s], so_lambda: λ₂x.t[x]

Latex:
\mforall{}[Info,B,A:Type]. \mforall{}P:B {}\mrightarrow{} \mBbbP{}. \mforall{}f:Id {}\mrightarrow{} 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. (single-valued-classrel(es;X;A) {}\mRightarrow{} single-valued-bag(init loc(e);B) {}\mRightarrow{} (\mforall{}v:B. (v \mdownarrow{}\mmember{} init loc(e) {}\mRightarrow{} P[v])) {}\mRightarrow{} (\mforall{}a:A. \mforall{}e':E. \mforall{}s:B. ((e' <loc e) {}\mRightarrow{} a \mmember{} X(e') {}\mRightarrow{} s \mmember{} Memory-loc-class(f;init;X)(e') {}\mRightarrow{} P[s] {}\mRightarrow{} P[f loc(e') a s])) {}\mRightarrow{} v \mmember{} Memory-loc-class(f;init;X)(e) {}\mRightarrow{} P[v]) Date html generated: 2016_05_17-AM-09_25_34 Last ObjectModification: 2015_12_29-PM-04_04_31 Theory : classrel!lemmas Home Index