Nuprl Lemma : reverse-bag
∀[T:Type]. ∀[b:bag(T)]. (rev(b) = b ∈ bag(T))
Proof
Definitions occuring in Statement :
bag: bag(T),
reverse: rev(as),
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
bag: bag(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
uimplies: b supposing a,
prop: ℙ,
guard: {T}
Lemmas referenced :
list_wf,
quotient-member-eq,
permutation_wf,
permutation-equiv,
reverse_wf,
equal_wf,
equal-wf-base,
bag_wf,
permutation-reverse,
permutation_inversion,
permutation_transitivity
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
because_Cache,
sqequalRule,
pertypeElimination,
productElimination,
thin,
equalityTransitivity,
hypothesis,
equalitySymmetry,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
lambdaFormation,
rename,
lambdaEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
productEquality,
isect_memberEquality,
axiomEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[b:bag(T)]. (rev(b) = b)
Date html generated:
2017_10_01-AM-08_44_58
Last ObjectModification:
2017_07_26-PM-04_30_27
Theory : bags
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