Nuprl Lemma : fpf-compatible-join2

[A:Type]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g,h:a:A fp-> B[a]].  (f ⊕ || h) supposing (g || and || h)


Definitions occuring in Statement :  fpf-join: f ⊕ g fpf-compatible: || 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 :  uall: [x:A]. B[x] member: t ∈ T uimplies: supposing a so_lambda: λ2x.t[x] so_apply: x[s] fpf-compatible: || g all: x:A. B[x] implies:  Q and: P ∧ Q subtype_rel: A ⊆B top: Top prop:
Lemmas referenced :  fpf-compatible-symmetry fpf-join_wf fpf-compatible-join assert_wf fpf-dom_wf top_wf subtype-fpf2 fpf-compatible_wf fpf_wf deq_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin hypothesisEquality sqequalRule lambdaEquality applyEquality hypothesis independent_isectElimination because_Cache dependent_functionElimination axiomEquality productEquality cumulativity lambdaFormation isect_memberEquality voidElimination voidEquality equalityTransitivity equalitySymmetry functionEquality universeEquality

\mforall{}[A:Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f,g,h:a:A  fp->  B[a]].
    (f  \moplus{}  g  ||  h)  supposing  (g  ||  h  and  f  ||  h)

Date html generated: 2018_05_21-PM-09_28_49
Last ObjectModification: 2018_02_09-AM-10_23_58

Theory : finite!partial!functions

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