Nuprl Lemma : fpf-compatible_monotonic-guard

[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f1,g1,f2,g2:a:A fp-> B[a]].
  ({f1 || g1 supposing f2 || g2}) supposing (g1 ⊆ g2 and f1 ⊆ f2)


Definitions occuring in Statement :  fpf-compatible: || g fpf-sub: f ⊆ g fpf: a:A fp-> B[a] deq: EqDecider(T) uimplies: supposing a uall: [x:A]. B[x] guard: {T} so_apply: x[s] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  guard: {T}
Lemmas referenced :  fpf-compatible_monotonic
Rules used in proof :  cut lemma_by_obid sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep hypothesis

\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[f1,g1,f2,g2:a:A  fp->  B[a]].
    (\{f1  ||  g1  supposing  f2  ||  g2\})  supposing  (g1  \msubseteq{}  g2  and  f1  \msubseteq{}  f2)

Date html generated: 2018_05_21-PM-09_20_01
Last ObjectModification: 2018_02_09-AM-10_17_49

Theory : finite!partial!functions

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