Nuprl Lemma : permutation-contains
∀[A:Type]. ∀L1,L2:A List. (permutation(A;L1;L2) ⇒ L2 ⊆ L1)
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
l_contains: A ⊆ B,
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],
implies: P ⇒ Q,
member: t ∈ T,
uimplies: b supposing a,
permutation: permutation(T;L1;L2),
exists: ∃x:A. B[x],
l_contains: A ⊆ B,
l_all: (∀x∈L.P[x]),
and: P ∧ Q,
prop: ℙ,
squash: ↓T,
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
permutation-length,
equal_wf,
list_wf,
l_member_wf,
permute_list_select,
decidable__lt,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
intformeq_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_wf,
iff_weakening_equal,
select_member,
int_seg_wf,
select_wf,
int_seg_properties,
decidable__le,
intformle_wf,
itermConstant_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
permute_list_length,
less_than_wf,
length_wf,
permutation_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
productElimination,
dependent_set_memberEquality,
because_Cache,
cumulativity,
equalityTransitivity,
equalitySymmetry,
applyEquality,
lambdaEquality,
imageElimination,
setElimination,
rename,
independent_pairFormation,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
imageMemberEquality,
baseClosed,
independent_functionElimination,
functionExtensionality,
hyp_replacement,
Error :applyLambdaEquality,
universeEquality
Latex:
\mforall{}[A:Type]. \mforall{}L1,L2:A List. (permutation(A;L1;L2) {}\mRightarrow{} L2 \msubseteq{} L1)
Date html generated:
2016_10_21-AM-10_17_29
Last ObjectModification:
2016_07_12-AM-05_32_58
Theory : list_1
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