Nuprl Lemma : remove-repeats-fun-as-remove-repeats-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,
all: ∀x:A. B[x],
top: Top,
remove-repeats-fun: remove-repeats-fun(eq;f;L),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
so_apply: x[s1;s2;s3],
squash: ↓T,
compose: f o g,
prop: ℙ,
deq: EqDecider(T),
true: True
Lemmas referenced :
list_induction,
equal_wf,
list_wf,
map_wf,
remove-repeats-fun_wf,
remove-repeats_wf,
map_nil_lemma,
remove_repeats_nil_lemma,
list_ind_nil_lemma,
nil_wf,
map_cons_lemma,
remove_repeats_cons_lemma,
list_ind_cons_lemma,
cons_wf,
filter-map,
filter_wf5,
l_member_wf,
bnot_wf,
deq_wf
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,
equalitySymmetry,
setElimination,
setEquality,
hyp_replacement,
Error :applyLambdaEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
axiomEquality,
functionEquality,
universeEquality
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:
2016_10_21-AM-10_39_56
Last ObjectModification:
2016_07_12-AM-05_50_00
Theory : decidable!equality
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