Nuprl Lemma : div_minus_one
∀[x:ℤ]. (x ÷ -1 ~ -x)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
divide: n ÷ m,
minus: -n,
natural_number: $n,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
int_nzero: ℤ-o,
true: True,
nequal: a ≠ b ∈ T ,
not: ¬A,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x],
guard: {T},
false: False,
subtype_rel: A ⊆r B,
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
equal_wf,
squash_wf,
true_wf,
istype-universe,
div_anti_sym,
nequal_wf,
subtype_rel_self,
iff_weakening_equal,
div_one,
istype-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
hypothesis,
applyEquality,
lambdaEquality_alt,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeIsType,
universeEquality,
dependent_set_memberEquality_alt,
natural_numberEquality,
lambdaFormation_alt,
dependent_functionElimination,
independent_functionElimination,
voidElimination,
equalityIstype,
inhabitedIsType,
baseClosed,
sqequalBase,
minusEquality,
sqequalRule,
imageMemberEquality,
because_Cache,
productElimination,
axiomSqEquality
Latex:
\mforall{}[x:\mBbbZ{}]. (x \mdiv{} -1 \msim{} -x)
Date html generated:
2020_05_19-PM-09_41_20
Last ObjectModification:
2019_12_26-PM-08_59_00
Theory : int_2
Home
Index