Nuprl Lemma : remove-repeats-l_contains
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[L1,L2:T List]. ||remove-repeats(eq;L1)|| ≤ ||remove-repeats(eq;L2)|| supposing L1 ⊆ L2
Proof
Definitions occuring in Statement :
remove-repeats: remove-repeats(eq;L),
l_contains: A ⊆ B,
length: ||as||,
list: T List,
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
le: A ≤ B,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
and: P ∧ Q,
l_contains: A ⊆ B,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
le: A ≤ B,
not: ¬A,
false: False
Lemmas referenced :
l_contains-no_repeats-length,
remove-repeats_wf,
remove-repeats_property,
l_all_iff,
l_member_wf,
member-remove-repeats,
less_than'_wf,
length_wf,
l_contains_wf,
list_wf,
deq_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
because_Cache,
dependent_functionElimination,
productElimination,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
independent_functionElimination,
lambdaFormation,
addLevel,
impliesFunctionality,
functionEquality,
independent_pairEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[L1,L2:T List].
||remove-repeats(eq;L1)|| \mleq{} ||remove-repeats(eq;L2)|| supposing L1 \msubseteq{} L2
Date html generated:
2016_05_14-PM-03_26_10
Last ObjectModification:
2015_12_26-PM-06_23_01
Theory : decidable!equality
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