Nuprl Lemma : fpf-map_wf
∀[A,C:Type]. ∀[B:A ⟶ Type]. ∀[x:a:A fp-> B[a]]. ∀[f:a:{a:A| (a ∈ fpf-domain(x))} ⟶ B[a] ⟶ C].
(fpf-map(a,v.f[a;v];x) ∈ C List)
Proof
Definitions occuring in Statement :
fpf-map: fpf-map(a,v.f[a; v];x),
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
so_apply: x[s1;s2],
so_apply: x[s],
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
top: Top,
prop: ℙ,
fpf-domain: fpf-domain(f),
fpf: a:A fp-> B[a],
fpf-map: fpf-map(a,v.f[a; v];x),
pi2: snd(t),
pi1: fst(t),
so_apply: x[s1;s2]
Lemmas referenced :
l_member_wf,
fpf-domain_wf,
subtype-fpf2,
top_wf,
fpf_wf,
map-wf2
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
sqequalHypSubstitution,
dependent_functionElimination,
hypothesisEquality,
hypothesis,
equalityTransitivity,
equalitySymmetry,
sqequalRule,
axiomEquality,
functionEquality,
setEquality,
lemma_by_obid,
isectElimination,
applyEquality,
lambdaEquality,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
setElimination,
rename,
cumulativity,
universeEquality,
productElimination
Latex:
\mforall{}[A,C:Type]. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[x:a:A fp-> B[a]]. \mforall{}[f:a:\{a:A| (a \mmember{} fpf-domain(x))\} {}\mrightarrow{} B[a] {}\mrightarrow{} C].
(fpf-map(a,v.f[a;v];x) \mmember{} C List)
Date html generated:
2018_05_21-PM-09_26_30
Last ObjectModification:
2018_02_09-AM-10_21_56
Theory : finite!partial!functions
Home
Index