Nuprl Lemma : sort-int-sorted
∀[T:Type]. ∀[as:T List]. sorted(sort-int(as)) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
sort-int: sort-int(as),
sorted: sorted(L),
list: T List,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
int: ℤ,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sort-int: sort-int(as),
sorted: sorted(L),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
int_seg: {i..j-},
guard: {T},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
length_of_nil_lemma,
le_weakening2,
subtype_rel_wf,
list_wf,
int_seg_wf,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_less_lemma,
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,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
length_wf,
int_seg_properties,
sort-int_wf,
select_wf,
less_than'_wf,
nil_wf,
merge-int-sorted
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
sqequalRule,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
because_Cache,
cumulativity,
setElimination,
rename,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
lambdaFormation
Latex:
\mforall{}[T:Type]. \mforall{}[as:T List]. sorted(sort-int(as)) supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_14-AM-07_36_16
Last ObjectModification:
2016_01_15-AM-08_44_20
Theory : list_1
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