Nuprl Lemma : fpf-union-compatible_wf

[A,C:Type]. ∀[B:A ⟶ Type].
  ∀[eq:EqDecider(A)]. ∀[f,g:x:A fp-> B[x] List]. ∀[R:(C List) ⟶ C ⟶ 𝔹].
    (fpf-union-compatible(A;C;x.B[x];eq;R;f;g) ∈ ℙ
  supposing ∀x:A. (B[x] ⊆C)


Proof




Definitions occuring in Statement :  fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g) fpf: a:A fp-> B[a] list: List deq: EqDecider(T) bool: 𝔹 uimplies: supposing a subtype_rel: A ⊆B uall: [x:A]. B[x] prop: so_apply: x[s] all: x:A. B[x] member: t ∈ T function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a fpf-union-compatible: fpf-union-compatible(A;C;x.B[x];eq;R;f;g) so_apply: x[s] so_lambda: λ2x.t[x] implies:  Q prop: subtype_rel: A ⊆B all: x:A. B[x] top: Top and: P ∧ Q or: P ∨ Q exists: x:A. B[x]

Latex:
\mforall{}[A,C:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].
    \mforall{}[eq:EqDecider(A)].  \mforall{}[f,g:x:A  fp->  B[x]  List].  \mforall{}[R:(C  List)  {}\mrightarrow{}  C  {}\mrightarrow{}  \mBbbB{}].
        (fpf-union-compatible(A;C;x.B[x];eq;R;f;g)  \mmember{}  \mBbbP{}) 
    supposing  \mforall{}x:A.  (B[x]  \msubseteq{}r  C)



Date html generated: 2016_05_16-AM-11_05_29
Last ObjectModification: 2015_12_29-AM-09_13_55

Theory : event-ordering


Home Index