Nuprl Lemma : sublist_append1
∀[T:Type]. ∀L1,L2:T List. L1 ⊆ L1 @ L2
Proof
Definitions occuring in Statement :
sublist: L1 ⊆ L2,
append: as @ bs,
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
sublist: L1 ⊆ L2,
exists: ∃x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
top: Top,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
prop: ℙ,
less_than: a < b,
cand: A c∧ B,
squash: ↓T,
guard: {T},
true: True,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
nat: ℕ,
so_apply: x[s]
Lemmas referenced :
length-append,
non_neg_length,
decidable__lt,
length_wf,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermConstant_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
lelt_wf,
append_wf,
int_seg_wf,
id_increasing,
length_wf_nat,
equal_wf,
squash_wf,
true_wf,
select_wf,
int_seg_properties,
decidable__le,
select_append_front,
iff_weakening_equal,
increasing_wf,
all_wf,
length_append,
subtype_rel_list,
top_wf,
nat_properties,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
dependent_pairFormation,
lambdaEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
hypothesisEquality,
productElimination,
independent_pairFormation,
hypothesis,
cut,
sqequalRule,
introduction,
extract_by_obid,
isectElimination,
isect_memberEquality,
voidElimination,
voidEquality,
because_Cache,
dependent_functionElimination,
addEquality,
cumulativity,
unionElimination,
natural_numberEquality,
independent_isectElimination,
int_eqEquality,
intEquality,
computeAll,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
imageMemberEquality,
baseClosed,
universeEquality,
independent_functionElimination,
productEquality,
functionExtensionality,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}L1,L2:T List. L1 \msubseteq{} L1 @ L2
Date html generated:
2017_04_14-AM-09_29_43
Last ObjectModification:
2017_02_27-PM-04_01_56
Theory : list_1
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