Nuprl Lemma : fpf-restrict-compatible
∀[A:Type]. ∀[P:A ⟶ 𝔹]. ∀[eq:EqDecider(A)]. ∀[B:A ⟶ Type]. ∀[f,g:x:A fp-> B[x]].
  fpf-restrict(f;P) || g supposing f || g
Proof
Definitions occuring in Statement : 
fpf-restrict: fpf-restrict(f;P)
, 
fpf-compatible: f || g
, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
bool: 𝔹
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
so_apply: x[s]
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
fpf-compatible: f || g
, 
all: ∀x:A. B[x]
, 
member: t ∈ T
, 
top: Top
, 
uall: ∀[x:A]. B[x]
, 
uimplies: b supposing a
, 
implies: P 
⇒ Q
, 
and: P ∧ Q
, 
cand: A c∧ B
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
, 
uiff: uiff(P;Q)
, 
guard: {T}
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
ap_fpf_restrict_lemma, 
fpf-restrict-dom, 
assert_wf, 
fpf-dom_wf, 
fpf-restrict_wf2, 
top_wf, 
subtype-fpf2, 
all_wf, 
equal_wf, 
fpf-ap_wf, 
fpf_wf, 
deq_wf, 
bool_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
cut, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
dependent_functionElimination, 
thin, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
hypothesis, 
isect_memberFormation, 
lambdaFormation, 
productElimination, 
hypothesisEquality, 
independent_functionElimination, 
isectElimination, 
because_Cache, 
lambdaEquality, 
applyEquality, 
functionExtensionality, 
cumulativity, 
independent_isectElimination, 
independent_pairFormation, 
productEquality, 
axiomEquality, 
functionEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[A:Type].  \mforall{}[P:A  {}\mrightarrow{}  \mBbbB{}].  \mforall{}[eq:EqDecider(A)].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[f,g:x:A  fp->  B[x]].
    fpf-restrict(f;P)  ||  g  supposing  f  ||  g
Date html generated:
2018_05_21-PM-09_31_30
Last ObjectModification:
2018_02_09-AM-10_25_52
Theory : finite!partial!functions
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