Nuprl Lemma : bag-drop-no-repeats
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[bs:bag(T)]. ∀[x:T]. bag-no-repeats(T;bag-drop(eq;bs;x)) supposing bag-no-repeats(T;bs)
Proof
Definitions occuring in Statement :
bag-drop: bag-drop(eq;bs;a),
bag-no-repeats: bag-no-repeats(T;bs),
bag: bag(T),
deq: EqDecider(T),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
and: P ∧ Q,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
bag-no-repeats: bag-no-repeats(T;bs),
uiff: uiff(P;Q)
Lemmas referenced :
bag-drop-property,
bag-no-repeats_wf,
squash_wf,
true_wf,
bag_wf,
iff_weakening_equal,
deq_wf,
bag-no-repeats-append,
single-bag_wf,
bag-drop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
equalityTransitivity,
hypothesis,
equalitySymmetry,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination,
cumulativity,
isect_memberEquality,
hyp_replacement,
Error :applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[bs:bag(T)]. \mforall{}[x:T].
bag-no-repeats(T;bag-drop(eq;bs;x)) supposing bag-no-repeats(T;bs)
Date html generated:
2016_10_25-AM-11_27_51
Last ObjectModification:
2016_07_12-AM-07_34_00
Theory : bags_2
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