Nuprl Lemma : glues-property2

∀[Info:Type]
  ∀es:EO+(Info)
    ∀[A,B:Type].
      ∀Ia:EClass(A). ∀Ib:EClass(B). ∀f:E(Ia) ⟶ B. ∀g:E(Ib) ⟶ E.
        (g glues Ia ──f⟶ Ib
        ⇒ {Bij(E(Ib);E(Ia);g)
           ∧ (∀e:E(Ib). g e c≤ e)
           ∧ (∀e,e':E(Ib).  (g e ≤loc g e'  ⇒ e ≤loc e' ))
           ∧ (∀e:E(Ib). ((f (g e)) = Ib(e) ∈ B))})

Proof

Definitions occuring in Statement : glues: g glues Ia ──f⟶ Ib, es-E-interface: E(X), eclass-val: X(e), eclass: EClass(A[eo; e]), event-ordering+: EO+(Info), es-causle: e c≤ e', es-le: e ≤loc e' , es-E: E, biject: Bij(A;B;f), uall: ∀[x:A]. B[x], guard: {T}, all: ∀x:A. B[x], implies: P ⇒ Q, and: P ∧ Q, apply: f a, function: x:A ⟶ B[x], universe: Type, equal: s = t ∈ T
Definitions unfolded in proof : top: Top, uimplies: b supposing a, so_apply: x[s1;s2], so_lambda: λ₂x y.t[x; y], subtype_rel: A ⊆r B, prop: ℙ, implies: P ⇒ Q, all: ∀x:A. B[x], member: t ∈ T, uall: ∀[x:A]. B[x], and: P ∧ Q, iff: P ⇐⇒ Q

Latex:
\mforall{}[Info:Type] \mforall{}es:EO+(Info) \mforall{}[A,B:Type]. \mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f:E(Ia) {}\mrightarrow{} B. \mforall{}g:E(Ib) {}\mrightarrow{} E. (g glues Ia {}{}f{}\mrightarrow{} Ib {}\mRightarrow{} \{Bij(E(Ib);E(Ia);g) \mwedge{} (\mforall{}e:E(Ib). g e c\mleq{} e) \mwedge{} (\mforall{}e,e':E(Ib). (g e \mleq{}loc g e' {}\mRightarrow{} e \mleq{}loc e' )) \mwedge{} (\mforall{}e:E(Ib). ((f (g e)) = Ib(e)))\}) Date html generated: 2016_05_17-AM-07_59_37 Last ObjectModification: 2015_12_28-PM-11_22_10 Theory : event-ordering Home Index