Nuprl Lemma : sorted-merge
∀[T:Type]. ∀[bs,as:T List]. sorted(merge(as;bs)) supposing sorted(as) supposing T ⊆r ℤ
Proof
Definitions occuring in Statement :
merge: merge(as;bs),
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,
so_lambda: λ2x.t[x],
prop: ℙ,
so_apply: x[s],
implies: P ⇒ Q,
merge: merge(as;bs),
all: ∀x:A. B[x],
top: Top,
sorted: sorted(L),
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
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],
less_than: a < b,
squash: ↓T,
subtype_rel: A ⊆r B
Lemmas referenced :
subtype_rel_wf,
s-insert_wf,
s-insert-sorted,
reduce_cons_lemma,
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,
select_wf,
less_than'_wf,
reduce_nil_lemma,
merge_wf,
sorted_wf,
isect_wf,
list_wf,
uall_wf,
list_induction
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesisEquality,
sqequalRule,
lambdaEquality,
hypothesis,
independent_isectElimination,
independent_functionElimination,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
independent_pairEquality,
because_Cache,
cumulativity,
setElimination,
rename,
natural_numberEquality,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
independent_pairFormation,
computeAll,
imageElimination,
applyEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[bs,as:T List]. sorted(merge(as;bs)) supposing sorted(as) supposing T \msubseteq{}r \mBbbZ{}
Date html generated:
2016_05_15-PM-03_52_39
Last ObjectModification:
2016_01_16-AM-10_56_34
Theory : general
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