Nuprl Lemma : fpf-compatible-join

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


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 fpf-compatible: || g all: x:A. B[x] implies:  Q and: P ∧ Q subtype_rel: A ⊆B so_lambda: λ2x.t[x] so_apply: x[s] top: Top prop: cand: c∧ B squash: T true: True guard: {T} iff: ⇐⇒ Q rev_implies:  Q bool: 𝔹 unit: Unit it: btrue: tt uiff: uiff(P;Q) ifthenelse: if then else fi  bfalse: ff or: P ∨ Q not: ¬A false: False
Lemmas referenced :  assert_wf fpf-dom_wf subtype-fpf2 top_wf fpf-join_wf fpf-compatible_wf fpf_wf deq_wf bool_wf equal-wf-T-base bnot_wf not_wf equal_wf squash_wf true_wf fpf-ap_wf fpf-join-ap iff_weakening_equal eqtt_to_assert uiff_transitivity eqff_to_assert assert_of_bnot fpf-join-dom
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution lambdaFormation hypothesisEquality sqequalRule lambdaEquality dependent_functionElimination thin axiomEquality hypothesis productEquality extract_by_obid isectElimination cumulativity applyEquality functionExtensionality independent_isectElimination isect_memberEquality voidElimination voidEquality because_Cache equalityTransitivity equalitySymmetry functionEquality universeEquality independent_functionElimination independent_pairFormation baseClosed productElimination imageElimination natural_numberEquality imageMemberEquality unionElimination equalityElimination

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

Date html generated: 2018_05_21-PM-09_28_24
Last ObjectModification: 2018_02_09-AM-10_23_43

Theory : finite!partial!functions

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