Nuprl Lemma : imax-list-member
∀L:ℤ List. (imax-list(L) ∈ L) supposing 0 < ||L||
Proof
Definitions occuring in Statement :
imax-list: imax-list(L),
l_member: (x ∈ l),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
all: ∀x:A. B[x],
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
imax-list: imax-list(L),
all: ∀x:A. B[x],
uimplies: b supposing a,
member: t ∈ T,
uall: ∀[x:A]. B[x],
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q,
prop: ℙ,
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
guard: {T},
or: P ∨ Q,
decidable: Dec(P),
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
subtype_rel: A ⊆r B,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
squash: ↓T,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
member-less_than,
length_wf,
combine-list-member,
imax_wf,
less_than_wf,
list_wf,
le_int_wf,
bool_wf,
eqtt_to_assert,
assert_of_le_int,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
equal-wf-base,
int_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
le_wf,
or_wf,
squash_wf,
true_wf,
imax_unfold,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
intEquality,
hypothesisEquality,
hypothesis,
independent_isectElimination,
rename,
dependent_functionElimination,
lambdaEquality,
independent_functionElimination,
because_Cache,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
productElimination,
inrFormation,
dependent_pairFormation,
int_eqEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
applyEquality,
promote_hyp,
instantiate,
cumulativity,
inlFormation,
imageElimination,
universeEquality,
imageMemberEquality,
baseClosed
Latex:
\mforall{}L:\mBbbZ{} List. (imax-list(L) \mmember{} L) supposing 0 < ||L||
Date html generated:
2017_04_14-AM-09_23_59
Last ObjectModification:
2017_02_27-PM-03_59_02
Theory : list_1
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