Nuprl Lemma : permutation-nil-iff
∀[A:Type]. ∀L:A List. (permutation(A;[];L) ⇐⇒ L = [] ∈ (A List))
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
or: P ∨ Q,
cons: [a / b],
top: Top,
ge: i ≥ j ,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A
Lemmas referenced :
permutation_wf,
nil_wf,
equal-wf-T-base,
list_wf,
permutation-length,
list-cases,
product_subtype_list,
length_of_nil_lemma,
length_of_cons_lemma,
non_neg_length,
satisfiable-full-omega-tt,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
itermAdd_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_term_value_add_lemma,
int_formula_prop_wf,
permutation-nil
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
independent_pairFormation,
cut,
hypothesis,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
baseClosed,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
promote_hyp,
hypothesis_subsumption,
productElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality
Latex:
\mforall{}[A:Type]. \mforall{}L:A List. (permutation(A;[];L) \mLeftarrow{}{}\mRightarrow{} L = [])
Date html generated:
2016_10_21-AM-10_17_38
Last ObjectModification:
2016_07_12-AM-05_32_48
Theory : list_1
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