Nuprl Lemma : append_cancel_wrt_permutation
∀[A:Type]. ∀as,bs,cs:A List. (permutation(A;as @ bs;as @ cs) ⇒ permutation(A;bs;cs))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
append: as @ bs,
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],
all: ∀x:A. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
append: as @ bs,
so_lambda: so_lambda(x,y,z.t[x; y; z]),
top: Top,
so_apply: x[s1;s2;s3],
guard: {T}
Lemmas referenced :
list_induction,
all_wf,
list_wf,
permutation_wf,
append_wf,
list_ind_nil_lemma,
list_ind_cons_lemma,
cons_cancel_wrt_permutation,
cons_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
functionEquality,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
rename,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}as,bs,cs:A List. (permutation(A;as @ bs;as @ cs) {}\mRightarrow{} permutation(A;bs;cs))
Date html generated:
2016_05_14-PM-02_21_14
Last ObjectModification:
2015_12_26-PM-04_28_08
Theory : list_1
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