Nuprl Lemma : remove-repeats-append
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L1,L2:T List]. (||remove-repeats(eq;L1 @ L2)|| = ||remove-repeats(eq;L2 @ L1)|| ∈ ℤ)
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
length: ||as||,
append: as @ bs,
list: T List,
deq: EqDecider(T),
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
remove-repeats-set-equal,
append_wf,
set-equal-permute
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
sqequalRule,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L1,L2:T List].
(||remove-repeats(eq;L1 @ L2)|| = ||remove-repeats(eq;L2 @ L1)||)
Date html generated:
2016_05_14-PM-03_26_15
Last ObjectModification:
2015_12_26-PM-06_23_02
Theory : decidable!equality
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