Nuprl Lemma : trivial-unsat-integer-inequality
∀[xs:ℤ List]. (¬xs ⋅ [-1] ≥0)
Proof
Definitions occuring in Statement :
satisfies-integer-inequality: xs ⋅ as ≥0,
cons: [a / b],
nil: [],
list: T List,
uall: ∀[x:A]. B[x],
not: ¬A,
minus: -n,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
false: False,
all: ∀x:A. B[x],
or: P ∨ Q,
satisfies-integer-inequality: xs ⋅ as ≥0,
top: Top,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
less_than': less_than'(a;b),
prop: ℙ,
ge: i ≥ j ,
cons: [a / b],
uimplies: b supposing a,
sq_type: SQType(T),
guard: {T},
le: A ≤ B,
true: True
Lemmas referenced :
list_wf,
nil_wf,
cons_wf,
satisfies-integer-inequality_wf,
length_wf,
equal_wf,
and_wf,
int_subtype_base,
subtype_base_sq,
int_dot_nil_left_lemma,
int_dot_cons_lemma,
reduce_hd_cons_lemma,
product_subtype_list,
ge_wf,
less_than_wf,
equal-wf-base,
int_dot_cons_nil_lemma,
length_of_cons_lemma,
length_of_nil_lemma,
list-cases
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
thin,
intEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
hypothesis,
dependent_functionElimination,
hypothesisEquality,
unionElimination,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
productElimination,
imageElimination,
productEquality,
baseClosed,
equalityTransitivity,
equalitySymmetry,
because_Cache,
promote_hyp,
hypothesis_subsumption,
instantiate,
cumulativity,
independent_isectElimination,
independent_functionElimination,
natural_numberEquality,
addEquality,
multiplyEquality,
minusEquality,
rename,
lambdaEquality
Latex:
\mforall{}[xs:\mBbbZ{} List]. (\mneg{}xs \mcdot{} [-1] \mgeq{}0)
Date html generated:
2016_05_14-AM-06_56_19
Last ObjectModification:
2016_01_14-PM-08_44_36
Theory : omega
Home
Index