Nuprl Lemma : permutation-singleton
∀[T:Type]. ∀[x:T]. ∀[ts:T List]. ts = [x] ∈ (T List) supposing permutation(T;[x];ts)
Proof
Definitions occuring in Statement :
permutation: permutation(T;L1;L2),
cons: [a / b],
nil: [],
list: T List,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
or: P ∨ Q,
top: Top,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
true: True,
false: False,
cons: [a / b],
squash: ↓T,
ge: i ≥ j ,
le: A ≤ B,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
prop: ℙ,
permutation: permutation(T;L1;L2),
permute_list: (L o f),
int_seg: {i..j-},
so_lambda: λ2x.t[x],
so_apply: x[s],
lelt: i ≤ j < k,
decidable: Dec(P),
less_than: a < b,
select: L[n]
Lemmas referenced :
top_wf,
length_cons_ge_one,
length_wf,
ge_wf,
squash_wf,
hd_wf,
reduce_hd_cons_lemma,
decidable__equal_int,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_not_lemma,
intformnot_wf,
lelt_wf,
int_seg_properties,
decidable__le,
set_subtype_base,
mklist-single,
list_wf,
permutation_wf,
int_formula_prop_wf,
int_term_value_add_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
itermAdd_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
non_neg_length,
product_subtype_list,
int_subtype_base,
subtype_base_sq,
length_of_nil_lemma,
length_of_cons_lemma,
list-cases,
nil_wf,
cons_wf,
permutation-length
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
because_Cache,
hypothesisEquality,
hypothesis,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
instantiate,
cumulativity,
intEquality,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
natural_numberEquality,
promote_hyp,
hypothesis_subsumption,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
imageMemberEquality,
baseClosed,
rename,
dependent_pairFormation,
int_eqEquality,
independent_pairFormation,
computeAll,
axiomEquality,
universeEquality,
setElimination,
setEquality,
dependent_set_memberEquality
Latex:
\mforall{}[T:Type]. \mforall{}[x:T]. \mforall{}[ts:T List]. ts = [x] supposing permutation(T;[x];ts)
Date html generated:
2016_05_14-PM-02_32_49
Last ObjectModification:
2016_01_15-AM-07_45_43
Theory : list_1
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