Nuprl Lemma : implies_l_member_append
∀T:Type. ∀l1,l2:T List. ∀v:T. (((v ∈ l1) ∨ (v ∈ l2)) ⇒ (v ∈ l1 @ l2))
Proof
Definitions occuring in Statement :
l_member: (x ∈ l),
append: as @ bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
l_member: (x ∈ l),
or: P ∨ Q,
exists: ∃x:A. B[x],
cand: A c∧ B,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
top: Top,
ge: i ≥ j ,
nat: ℕ,
decidable: Dec(P),
false: False,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
squash: ↓T,
int_seg: {i..j-},
lelt: i ≤ j < k,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
so_lambda: λ2x.t[x],
so_apply: x[s],
uiff: uiff(P;Q),
less_than: a < b,
subtract: n - m
Lemmas referenced :
l_member_wf,
list_wf,
istype-universe,
length-append,
istype-void,
non_neg_length,
nat_properties,
decidable__lt,
length_wf,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformless_wf,
itermVar_wf,
itermAdd_wf,
intformle_wf,
itermConstant_wf,
istype-int,
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,
equal_wf,
squash_wf,
true_wf,
select_append_front,
decidable__le,
le_wf,
istype-less_than,
subtype_rel_self,
iff_weakening_equal,
append_wf,
select_wf,
add_nat_wf,
length_wf_nat,
add-is-int-iff,
set_subtype_base,
int_subtype_base,
intformeq_wf,
int_formula_prop_eq_lemma,
false_wf,
select_append_back,
add-associates,
minus-one-mul,
add-swap,
add-mul-special,
zero-mul,
add-zero
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
sqequalHypSubstitution,
unionElimination,
thin,
productElimination,
sqequalRule,
Error :unionIsType,
Error :universeIsType,
cut,
introduction,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
Error :inhabitedIsType,
instantiate,
universeEquality,
Error :dependent_pairFormation_alt,
Error :isect_memberEquality_alt,
voidElimination,
because_Cache,
setElimination,
rename,
dependent_functionElimination,
addEquality,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :lambdaEquality_alt,
int_eqEquality,
independent_pairFormation,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
Error :dependent_set_memberEquality_alt,
Error :productIsType,
imageMemberEquality,
baseClosed,
Error :equalityIsType1,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
intEquality,
baseApply,
closedConclusion
Latex:
\mforall{}T:Type. \mforall{}l1,l2:T List. \mforall{}v:T. (((v \mmember{} l1) \mvee{} (v \mmember{} l2)) {}\mRightarrow{} (v \mmember{} l1 @ l2))
Date html generated:
2019_06_20-PM-02_57_09
Last ObjectModification:
2018_10_17-AM-10_43_40
Theory : continuity
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