Nuprl Lemma : remove-repeats-fun-sublist
∀[A,B:Type]. ∀eq:EqDecider(B). ∀f:A ⟶ B. ∀L:A List. remove-repeats-fun(eq;f;L) ⊆ L
Proof
Definitions occuring in Statement :
remove-repeats-fun: remove-repeats-fun(eq;f;L),
sublist: L1 ⊆ L2,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀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),
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
prop: ℙ,
deq: EqDecider(T),
or: P ∨ Q,
and: P ∧ Q,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
list_induction,
sublist_wf,
remove-repeats-fun_wf,
list_wf,
list_ind_nil_lemma,
nil-sublist,
list_ind_cons_lemma,
deq_wf,
filter_wf5,
bnot_wf,
l_member_wf,
filter_is_sublist,
sublist_transitivity,
cons_wf,
cons_sublist_cons
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
rename,
because_Cache,
functionEquality,
universeEquality,
applyEquality,
setElimination,
setEquality,
inlFormation,
independent_pairFormation,
productElimination
Latex:
\mforall{}[A,B:Type]. \mforall{}eq:EqDecider(B). \mforall{}f:A {}\mrightarrow{} B. \mforall{}L:A List. remove-repeats-fun(eq;f;L) \msubseteq{} L
Date html generated:
2016_05_14-PM-03_28_30
Last ObjectModification:
2015_12_26-PM-06_24_22
Theory : decidable!equality
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