Nuprl Lemma : fpf-compatible-mod_wf
∀[A:Type]. ∀[B:A ⟶ Type]. ∀[eq:EqDecider(A)]. ∀[f,g:a:A fp-> B[a]]. ∀[R:⋂a:A. (B[a] ⟶ B[a] ⟶ 𝔹)].
  (fpf-compatible-mod(A;a.B[a];eq;
   R;f;g) ∈ ℙ)
Proof
Definitions occuring in Statement : 
fpf-compatible-mod: fpf-compatible-mod, 
fpf: a:A fp-> B[a]
, 
deq: EqDecider(T)
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
member: t ∈ T
, 
isect: ⋂x:A. B[x]
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
fpf-compatible-mod: fpf-compatible-mod, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
top: Top
Lemmas referenced : 
all_wf, 
assert_wf, 
fpf-dom_wf, 
subtype-fpf2, 
top_wf, 
not_wf, 
fpf-ap_wf, 
equal_wf, 
bool_wf, 
fpf_wf, 
deq_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
cumulativity, 
hypothesisEquality, 
lambdaEquality, 
functionEquality, 
productEquality, 
because_Cache, 
applyEquality, 
functionExtensionality, 
hypothesis, 
independent_isectElimination, 
lambdaFormation, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
equalityTransitivity, 
equalitySymmetry, 
productElimination, 
axiomEquality, 
isectEquality, 
universeEquality
Latex:
\mforall{}[A:Type].  \mforall{}[B:A  {}\mrightarrow{}  Type].  \mforall{}[eq:EqDecider(A)].  \mforall{}[f,g:a:A  fp->  B[a]].  \mforall{}[R:\mcap{}a:A.  (B[a]  {}\mrightarrow{}  B[a]  {}\mrightarrow{}  \mBbbB{})].
    (fpf-compatible-mod(A;a.B[a];eq;
      R;f;g)  \mmember{}  \mBbbP{})
Date html generated:
2018_05_21-PM-09_20_05
Last ObjectModification:
2018_02_09-AM-10_17_51
Theory : finite!partial!functions
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