Nuprl Lemma : permutation_functionality_wrt_permutation
∀[A:Type]
∀as1,as2,bs1,bs2:A List.
(permutation(A;as1;as2) ⇒ permutation(A;bs1;bs2) ⇒ (permutation(A;as1;bs1) ⇐⇒ permutation(A;as2;bs2)))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
list: T List,
uall: ∀[x:A]. B[x],
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
guard: {T},
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
permutation_inversion,
permutation_transitivity,
permutation_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
dependent_functionElimination,
independent_functionElimination,
hypothesis,
universeEquality
Latex:
\mforall{}[A:Type]
\mforall{}as1,as2,bs1,bs2:A List.
(permutation(A;as1;as2)
{}\mRightarrow{} permutation(A;bs1;bs2)
{}\mRightarrow{} (permutation(A;as1;bs1) \mLeftarrow{}{}\mRightarrow{} permutation(A;as2;bs2)))
Date html generated:
2016_05_14-PM-02_20_10
Last ObjectModification:
2015_12_26-PM-04_28_23
Theory : list_1
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