Nuprl Lemma : remove-repeats-fun-map
∀[A,B:Type]. ∀[eq:EqDecider(B)]. ∀[f:A ⟶ B]. ∀[L:A List].
(map(f;remove-repeats-fun(eq;f;L)) = remove-repeats(eq;map(f;L)) ∈ (B List))
Proof
Definitions occuring in Statement :
remove-repeats-fun: remove-repeats-fun(eq;f;L),
remove-repeats: remove-repeats(eq;L),
map: map(f;as),
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
remove-repeats-fun: remove-repeats-fun(eq;f;L),
all: ∀x:A. B[x],
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
squash: ↓T,
true: True,
prop: ℙ,
deq: EqDecider(T),
compose: f o g,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
equal_wf,
list_wf,
map_wf,
remove-repeats-fun_wf,
remove-repeats_wf,
list_ind_nil_lemma,
map_nil_lemma,
remove_repeats_nil_lemma,
nil_wf,
list_ind_cons_lemma,
map_cons_lemma,
remove_repeats_cons_lemma,
cons_wf,
deq_wf,
filter_wf5,
l_member_wf,
bnot_wf,
set_wf,
filter-map,
squash_wf,
true_wf,
bool_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
cumulativity,
hypothesis,
functionExtensionality,
applyEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
lambdaFormation,
rename,
imageElimination,
because_Cache,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
functionEquality,
universeEquality,
equalityUniverse,
levelHypothesis,
setElimination,
setEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}[eq:EqDecider(B)]. \mforall{}[f:A {}\mrightarrow{} B]. \mforall{}[L:A List].
(map(f;remove-repeats-fun(eq;f;L)) = remove-repeats(eq;map(f;L)))
Date html generated:
2017_04_17-AM-09_12_11
Last ObjectModification:
2017_02_27-PM-05_19_27
Theory : decidable!equality
Home
Index