Nuprl Lemma : l_member_functionality_wrt_permutation
∀[A:Type]. ∀as,bs:A List. ∀a:A. (permutation(A;as;bs) ⇒ (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],
all: ∀x:A. B[x],
implies: P ⇒ Q,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q
Lemmas referenced :
member-permutation,
l_member_wf,
permutation_wf,
list_wf
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaFormation,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
universeEquality,
productElimination
Latex:
\mforall{}[A:Type]. \mforall{}as,bs:A List. \mforall{}a:A. (permutation(A;as;bs) {}\mRightarrow{} (a \mmember{} as) {}\mRightarrow{} (a \mmember{} bs))
Date html generated:
2016_05_14-PM-02_22_00
Last ObjectModification:
2015_12_26-PM-04_27_01
Theory : list_1
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