Nuprl Lemma : permutation-nil
∀[A:Type]. permutation(A;[];[])
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
nil: [],
uall: ∀[x:A]. B[x],
universe: Type
Definitions unfolded in proof :
permutation: permutation(T;L1;L2),
uall: ∀[x:A]. B[x],
exists: ∃x:A. B[x],
member: t ∈ T,
permute_list: (L o f),
inject: Inj(A;B;f),
select: L[n],
uimplies: b supposing a,
all: ∀x:A. B[x],
nil: [],
it: ⋅,
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
mklist: mklist(n;f),
and: P ∧ Q,
cand: A c∧ B,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
list_wf,
all_wf,
and_wf,
equal_wf,
primrec0_lemma,
base_wf,
stuck-spread,
length_of_nil_lemma,
nil_wf,
length_wf,
int_seg_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
dependent_pairFormation,
lambdaEquality,
hypothesisEquality,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
voidEquality,
hypothesis,
baseClosed,
independent_isectElimination,
lambdaFormation,
isect_memberEquality,
voidElimination,
dependent_functionElimination,
independent_pairFormation,
functionEquality,
applyEquality,
because_Cache,
universeEquality
Latex:
\mforall{}[A:Type]. permutation(A;[];[])
Date html generated:
2016_05_14-PM-02_18_18
Last ObjectModification:
2016_01_15-AM-07_54_48
Theory : list_1
Home
Index