Nuprl Lemma : strict-majority-or-max_wf
∀[L:ℤ List]. (strict-majority-or-max(L) ∈ ℤ)
Proof
Definitions occuring in Statement :
strict-majority-or-max: strict-majority-or-max(L),
list: T List,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
strict-majority-or-max: strict-majority-or-max(L),
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
prop: ℙ,
bfalse: ff,
iff: P ⇐⇒ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
or: P ∨ Q,
cons: [a / b],
top: Top,
guard: {T},
nat: ℕ,
le: A ≤ B,
decidable: Dec(P),
subtract: n - m,
less_than': less_than'(a;b),
true: True
Lemmas referenced :
null_wf,
bool_wf,
uiff_transitivity,
equal-wf-base,
list_subtype_base,
int_subtype_base,
assert_wf,
list_wf,
eqtt_to_assert,
assert_of_null,
strict-majority_wf,
int-deq_wf,
unit_wf2,
equal_wf,
iff_transitivity,
bnot_wf,
not_wf,
iff_weakening_uiff,
eqff_to_assert,
assert_of_bnot,
imax-list_wf,
list-cases,
length_of_nil_lemma,
nil_wf,
product_subtype_list,
length_of_cons_lemma,
length_wf_nat,
nat_wf,
decidable__lt,
false_wf,
not-lt-2,
condition-implies-le,
minus-add,
minus-one-mul,
zero-add,
minus-one-mul-top,
add-commutes,
add_functionality_wrt_le,
add-associates,
add-zero,
le-add-cancel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
intEquality,
hypothesisEquality,
hypothesis,
lambdaFormation,
unionElimination,
equalityElimination,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
independent_isectElimination,
independent_functionElimination,
because_Cache,
productElimination,
unionEquality,
equalityTransitivity,
equalitySymmetry,
natural_numberEquality,
dependent_functionElimination,
independent_pairFormation,
impliesFunctionality,
voidElimination,
promote_hyp,
hypothesis_subsumption,
isect_memberEquality,
voidEquality,
setElimination,
rename,
addEquality,
lambdaEquality,
minusEquality,
axiomEquality
Latex:
\mforall{}[L:\mBbbZ{} List]. (strict-majority-or-max(L) \mmember{} \mBbbZ{})
Date html generated:
2019_06_20-PM-01_55_00
Last ObjectModification:
2018_08_21-PM-01_55_26
Theory : decidable!equality
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