Nuprl Lemma : es-interface-map-val

[Info,A:Type]. ∀[es:EO+(Info)]. ∀[X:EClass(A)]. ∀[f:A ⟶ E(X) ⟶ bag(Top)]. ∀[e:E].
  es-interface-map(f;X)(e) only(f X(e) e) supposing ↑e ∈b es-interface-map(f;X)


Proof




Definitions occuring in Statement :  es-interface-map: es-interface-map(f;X) es-E-interface: E(X) eclass-val: X(e) in-eclass: e ∈b X eclass: EClass(A[eo; e]) event-ordering+: EO+(Info) es-E: E assert: b uimplies: supposing a uall: [x:A]. B[x] top: Top apply: a function: x:A ⟶ B[x] universe: Type sqequal: t bag-only: only(bs) bag: bag(T)
Definitions unfolded in proof :  uall: [x:A]. B[x] eclass-val: X(e) es-interface-map: es-interface-map(f;X) in-eclass: e ∈b X let: let member: t ∈ T eclass: EClass(A[eo; e]) subtype_rel: A ⊆B all: x:A. B[x] implies:  Q exposed-it: exposed-it bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a nat: ifthenelse: if then else fi  bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False eq_int: (i =z j) so_lambda: λ2y.t[x; y] so_apply: x[s1;s2] top: Top cand: c∧ B decidable: Dec(P) satisfiable_int_formula: satisfiable_int_formula(fmla) not: ¬A rev_uimplies: rev_uimplies(P;Q) es-E-interface: E(X)

Latex:
\mforall{}[Info,A:Type].  \mforall{}[es:EO+(Info)].  \mforall{}[X:EClass(A)].  \mforall{}[f:A  {}\mrightarrow{}  E(X)  {}\mrightarrow{}  bag(Top)].  \mforall{}[e:E].
    es-interface-map(f;X)(e)  \msim{}  only(f  X(e)  e)  supposing  \muparrow{}e  \mmember{}\msubb{}  es-interface-map(f;X)



Date html generated: 2016_05_16-PM-10_33_30
Last ObjectModification: 2016_01_17-PM-07_23_28

Theory : event-ordering


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