Nuprl Lemma : fpf-compatible_monotonic

[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f1,g1,f2,g2:a:A fp-> B[a]].
  (f1 || g1) supposing (f2 || g2 and 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] so_apply: x[s] function: x:A ⟶ B[x] universe: Type
Definitions unfolded in proof :  fpf-compatible: || g fpf-sub: f ⊆ g uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a all: x:A. B[x] implies:  Q and: P ∧ Q cand: c∧ B prop: subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] top: Top guard: {T}
Lemmas referenced :  assert_wf fpf-dom_wf subtype-fpf2 top_wf all_wf equal_wf fpf-ap_wf deq_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lambdaFormation sqequalHypSubstitution productElimination thin hypothesis dependent_functionElimination hypothesisEquality independent_functionElimination independent_pairFormation equalityElimination because_Cache equalityTransitivity equalitySymmetry productEquality extract_by_obid isectElimination cumulativity applyEquality lambdaEquality functionExtensionality independent_isectElimination isect_memberEquality voidElimination voidEquality axiomEquality functionEquality

\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  and  g1  \msubseteq{}  g2  and  f1  \msubseteq{}  f2)

Date html generated: 2018_05_21-PM-09_19_59
Last ObjectModification: 2018_02_09-AM-10_17_48

Theory : finite!partial!functions

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