Nuprl Lemma : sorted-by_wf
∀[T:Type]. ∀[L:T List]. ∀[R:{x:T| (x ∈ L)} ⟶ {x:T| (x ∈ L)} ⟶ ℙ]. (sorted-by(R;L) ∈ ℙ)
Proof
Definitions occuring in Statement :
sorted-by: sorted-by(R;L),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
sorted-by: sorted-by(R;L),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
prop: ℙ,
uimplies: b supposing a,
guard: {T},
lelt: i ≤ j < k,
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
less_than: a < b,
squash: ↓T,
so_apply: x[s]
Lemmas referenced :
list_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
int_seg_properties,
list-subtype,
l_member_wf,
select_wf,
length_wf,
int_seg_wf,
all_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
cumulativity,
hypothesisEquality,
hypothesis,
lambdaEquality,
because_Cache,
setElimination,
rename,
applyEquality,
setEquality,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
axiomEquality,
functionEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[L:T List]. \mforall{}[R:\{x:T| (x \mmember{} L)\} {}\mrightarrow{} \{x:T| (x \mmember{} L)\} {}\mrightarrow{} \mBbbP{}]. (sorted-by(R;L) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-01_46_41
Last ObjectModification:
2016_01_15-AM-08_20_11
Theory : list_1
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