Nuprl Lemma : unshuffle-iseg
∀[T:Type]. ∀as,bs:T List. (as ≤ bs ⇒ unshuffle(as) ≤ unshuffle(bs))
Proof
Definitions occuring in Statement :
unshuffle: unshuffle(L),
iseg: l1 ≤ l2,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
member: t ∈ T,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
subtype_rel: A ⊆r B,
le: A ≤ B,
less_than': less_than'(a;b),
nat: ℕ,
ge: i ≥ j ,
less_than: a < b,
squash: ↓T,
so_lambda: λ2x.t[x],
so_apply: x[s],
unshuffle: unshuffle(L),
lt_int: i <z j,
ifthenelse: if b then t else f fi ,
btrue: tt,
cons: [a / b],
iff: P ⇐⇒ Q,
assert: ↑b,
bfalse: ff,
bool: 𝔹,
unit: Unit,
it: ⋅,
uiff: uiff(P;Q),
sq_type: SQType(T),
bnot: ¬bb,
rev_implies: P ⇐ Q,
cand: A c∧ B
Lemmas referenced :
int_seg_properties,
satisfiable-full-omega-tt,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
decidable__equal_int,
subtract_wf,
int_seg_subtype,
false_wf,
decidable__le,
intformnot_wf,
itermSubtract_wf,
intformeq_wf,
int_formula_prop_not_lemma,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
le_wf,
length_wf,
non_neg_length,
nat_properties,
decidable__lt,
lelt_wf,
less_than_wf,
iseg_wf,
all_wf,
list_wf,
unshuffle_wf,
set_wf,
primrec-wf2,
nat_wf,
itermAdd_wf,
int_term_value_add_lemma,
length_wf_nat,
list-cases,
length_of_nil_lemma,
reduce_tl_nil_lemma,
nil_iseg,
product_subtype_list,
iseg_nil,
cons_wf,
null_cons_lemma,
cons_iseg,
length_of_cons_lemma,
reduce_hd_cons_lemma,
reduce_tl_cons_lemma,
lt_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_lt_int,
iseg_weakening,
nil_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
cut,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
natural_numberEquality,
because_Cache,
hypothesisEquality,
hypothesis,
setElimination,
rename,
productElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
unionElimination,
addLevel,
applyEquality,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
levelHypothesis,
hypothesis_subsumption,
dependent_set_memberEquality,
cumulativity,
imageElimination,
independent_functionElimination,
functionEquality,
productEquality,
addEquality,
universeEquality,
promote_hyp,
equalityElimination,
instantiate,
independent_pairEquality
Latex:
\mforall{}[T:Type]. \mforall{}as,bs:T List. (as \mleq{} bs {}\mRightarrow{} unshuffle(as) \mleq{} unshuffle(bs))
Date html generated:
2017_04_17-AM-08_58_11
Last ObjectModification:
2017_02_27-PM-05_13_25
Theory : list_1
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