Nuprl Lemma : no_repeats-sublist
∀[T:Type]. ∀[L,L':T List]. (no_repeats(T;L')) supposing (L' ⊆ L and no_repeats(T;L))
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
no_repeats: no_repeats(T;l),
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
guard: {T},
all: ∀x:A. B[x]
Lemmas referenced :
equal_wf,
l_before_wf,
sublist_wf,
uall_wf,
isect_wf,
not_wf,
iff_weakening_uiff,
no_repeats_wf,
no_repeats_iff,
no_repeats_witness,
list_wf,
l_before_sublist
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
lambdaFormation,
thin,
hypothesis,
sqequalHypSubstitution,
independent_functionElimination,
voidElimination,
extract_by_obid,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
because_Cache,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
addLevel,
independent_isectElimination,
productElimination,
cumulativity,
isectEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L,L':T List]. (no\_repeats(T;L')) supposing (L' \msubseteq{} L and no\_repeats(T;L))
Date html generated:
2019_06_20-PM-01_27_21
Last ObjectModification:
2018_08_24-PM-11_25_48
Theory : list_1
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