Nuprl Lemma : permute_list_wf
∀[T:Type]. ∀[L:T List]. ∀[f:ℕ||L|| ⟶ ℕ||L||]. ((L o f) ∈ T List)
Proof
Definitions occuring in Statement :
permute_list: (L o f),
length: ||as||,
list: T List,
int_seg: {i..j-},
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
permute_list: (L o f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
ge: i ≥ j ,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
nat: ℕ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top
Lemmas referenced :
list_wf,
int_seg_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_not_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_and_lemma,
intformnot_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformand_wf,
satisfiable-full-omega-tt,
le_wf,
nat_properties,
lelt_wf,
decidable__le,
length_wf,
int_seg_properties,
non_neg_length,
select_wf,
length_wf_nat,
mklist_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
cumulativity,
hypothesisEquality,
because_Cache,
hypothesis,
lambdaEquality,
applyEquality,
independent_isectElimination,
natural_numberEquality,
setElimination,
rename,
productElimination,
dependent_functionElimination,
dependent_set_memberEquality,
independent_pairFormation,
unionElimination,
equalityTransitivity,
equalitySymmetry,
setEquality,
intEquality,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[f:\mBbbN{}||L|| {}\mrightarrow{} \mBbbN{}||L||]. ((L o f) \mmember{} T List)
Date html generated:
2016_05_14-PM-02_16_54
Last ObjectModification:
2016_01_15-AM-07_56_36
Theory : list_1
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