Nuprl Lemma : fpf-compatible-join-iff

[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ─→ Type]. ∀[f,g,h:a:A fp-> B[a]].
  uiff(h || f ⊕ g;h || f ∧ || g) supposing || g


Proof




Definitions occuring in Statement :  fpf-join: f ⊕ g fpf-compatible: || g fpf: a:A fp-> B[a] deq: EqDecider(T) uiff: uiff(P;Q) uimplies: supposing a uall: [x:A]. B[x] so_apply: x[s] and: P ∧ Q function: x:A ─→ B[x] universe: Type
Lemmas :  assert_wf fpf-dom_wf subtype-fpf2 top_wf subtype_top fpf-compatible_wf fpf-join_wf fpf-compatible-join fpf_wf deq_wf fpf-join-dom fpf-join-ap-left iff_weakening_equal fpf-join-ap bool_cases subtype_base_sq bool_wf bool_subtype_base eqtt_to_assert eqff_to_assert assert_of_bnot
\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f,g,h:a:A  fp->  B[a]].
    uiff(h  ||  f  \moplus{}  g;h  ||  f  \mwedge{}  h  ||  g)  supposing  f  ||  g



Date html generated: 2015_07_17-AM-11_12_13
Last ObjectModification: 2015_02_04-PM-05_06_51

Home Index