Nuprl Lemma : permutation-equiv
∀[A:Type]. EquivRel(A List)(permutation(A;_1;_2))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
list: T List,
equiv_rel: EquivRel(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
member: t ∈ T,
sym: Sym(T;x,y.E[x; y]),
implies: P ⇒ Q,
prop: ℙ,
trans: Trans(T;x,y.E[x; y]),
uimplies: b supposing a
Lemmas referenced :
list_wf,
permutation_inversion,
permutation_wf,
permutation_transitivity,
permutation_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
independent_pairFormation,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
dependent_functionElimination,
independent_functionElimination,
universeEquality,
independent_isectElimination
Latex:
\mforall{}[A:Type]. EquivRel(A List)(permutation(A;$_{1}$;$_{2}$))
Date html generated:
2016_05_14-PM-02_19_24
Last ObjectModification:
2015_12_26-PM-04_28_31
Theory : list_1
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