Nuprl Lemma : member-permutation
∀[A:Type]. ∀as,bs:A List. (permutation(A;as;bs) ⇒ {∀a:A. ((a ∈ as) ⇐⇒ (a ∈ bs))})
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
guard: {T},
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
guard: {T},
prop: ℙ,
l_contains: A ⊆ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
permutation_inversion,
permutation-contains,
permutation_wf,
list_wf,
l_all_iff,
l_member_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
because_Cache,
universeEquality,
sqequalRule,
lambdaEquality,
setElimination,
rename,
setEquality,
productElimination,
independent_pairFormation
Latex:
\mforall{}[A:Type]. \mforall{}as,bs:A List. (permutation(A;as;bs) {}\mRightarrow{} \{\mforall{}a:A. ((a \mmember{} as) \mLeftarrow{}{}\mRightarrow{} (a \mmember{} bs))\})
Date html generated:
2016_05_14-PM-02_21_52
Last ObjectModification:
2015_12_26-PM-04_27_32
Theory : list_1
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