Nuprl Lemma : before_last_or
∀[T:Type]. ∀L:T List. ∀x:T. ((x ∈ L) ⇒ ((x = last(L) ∈ T) ∨ x before last(L) ∈ L))
Proof
Definitions occuring in Statement :
l_before: x before y ∈ l,
last: last(L),
l_member: (x ∈ l),
list: T List,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
or: P ∨ Q,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
l_member: (x ∈ l),
exists: ∃x:A. B[x],
cand: A c∧ B,
member: t ∈ T,
nat: ℕ,
decidable: Dec(P),
or: P ∨ Q,
prop: ℙ,
and: P ∧ Q,
ge: i ≥ j ,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
not: ¬A,
top: Top,
true: True,
last: last(L),
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
less_than: a < b,
le: A ≤ B,
uiff: uiff(P;Q)
Lemmas referenced :
decidable__equal_int,
subtract_wf,
length_wf,
l_member_wf,
list_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
l_before_wf,
equal_wf,
squash_wf,
true_wf,
select_wf,
le_wf,
less_than_wf,
iff_weakening_equal,
l_before_select,
itermSubtract_wf,
intformless_wf,
int_term_value_subtract_lemma,
int_formula_prop_less_lemma,
decidable__lt,
lelt_wf,
intformeq_wf,
int_formula_prop_eq_lemma,
last_wf,
non_null_iff_length,
subtype_rel_list,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
cut,
introduction,
extract_by_obid,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
cumulativity,
natural_numberEquality,
unionElimination,
universeEquality,
because_Cache,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
inlFormation,
equalityTransitivity,
equalitySymmetry,
applyEquality,
imageElimination,
productEquality,
imageMemberEquality,
baseClosed,
independent_functionElimination,
inrFormation,
dependent_set_memberEquality,
hyp_replacement,
applyLambdaEquality
Latex:
\mforall{}[T:Type]. \mforall{}L:T List. \mforall{}x:T. ((x \mmember{} L) {}\mRightarrow{} ((x = last(L)) \mvee{} x before last(L) \mmember{} L))
Date html generated:
2017_04_17-AM-07_36_31
Last ObjectModification:
2017_02_27-PM-04_10_54
Theory : list_1
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