Nuprl Lemma : es-interface-filter_wf

[Info,A:Type]. ∀[X:EClass(A)]. ∀[P:A ⟶ 𝔹].  (X|a.P[a] ∈ EClass({a:A| ↑P[a]} ))


Proof




Definitions occuring in Statement :  es-interface-filter: X|a.P[a] eclass: EClass(A[eo; e]) assert: b bool: 𝔹 uall: [x:A]. B[x] so_apply: x[s] member: t ∈ T set: {x:A| B[x]}  function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T es-interface-filter: X|a.P[a] eclass: EClass(A[eo; e]) eclass-compose1: X subtype_rel: A ⊆B all: x:A. B[x] implies:  Q bool: 𝔹 unit: Unit it: btrue: tt ifthenelse: if then else fi  uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a so_lambda: λ2x.t[x] so_apply: x[s] bfalse: ff exists: x:A. B[x] prop: or: P ∨ Q sq_type: SQType(T) guard: {T} bnot: ¬bb assert: b false: False so_lambda: λ2y.t[x; y] so_apply: x[s1;s2]

Latex:
\mforall{}[Info,A:Type].  \mforall{}[X:EClass(A)].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].    (X|a.P[a]  \mmember{}  EClass(\{a:A|  \muparrow{}P[a]\}  ))



Date html generated: 2016_05_16-PM-10_51_32
Last ObjectModification: 2015_12_29-AM-10_47_17

Theory : event-ordering


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