Nuprl Lemma : trivial-cancel
∀[g:ℤ-o]. ∀[v:ℤ].  uiff((g * v) = 0 ∈ ℤ;v = 0 ∈ ℤ)
Proof
Definitions occuring in Statement : 
int_nzero: ℤ-o
, 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
multiply: n * m
, 
natural_number: $n
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
subtype_rel: A ⊆r B
, 
int_nzero: ℤ-o
, 
prop: ℙ
, 
uimplies: b supposing a
, 
and: P ∧ Q
, 
uiff: uiff(P;Q)
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
nequal: a ≠ b ∈ T 
, 
squash: ↓T
, 
true: True
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
top: Top
, 
all: ∀x:A. B[x]
, 
sq_type: SQType(T)
Lemmas referenced : 
int_nzero_wf, 
int_subtype_base, 
equal-wf-base, 
equal-wf-T-base, 
equal_wf, 
zero-div-rem, 
squash_wf, 
true_wf, 
divide-exact, 
subtype_rel_self, 
iff_weakening_equal, 
zero-mul, 
mul-commutes, 
subtype_base_sq
Rules used in proof : 
equalitySymmetry, 
equalityTransitivity, 
axiomEquality, 
isect_memberEquality, 
independent_pairEquality, 
productElimination, 
sqequalRule, 
applyEquality, 
because_Cache, 
baseClosed, 
hypothesisEquality, 
rename, 
setElimination, 
multiplyEquality, 
intEquality, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
extract_by_obid, 
hypothesis, 
independent_pairFormation, 
cut, 
introduction, 
isect_memberFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
natural_numberEquality, 
voidElimination, 
independent_functionElimination, 
lambdaFormation, 
divideEquality, 
applyLambdaEquality, 
Error :lambdaEquality_alt, 
imageElimination, 
Error :universeIsType, 
Error :inhabitedIsType, 
universeEquality, 
imageMemberEquality, 
instantiate, 
independent_isectElimination, 
voidEquality, 
lambdaEquality, 
dependent_functionElimination, 
cumulativity
Latex:
\mforall{}[g:\mBbbZ{}\msupminus{}\msupzero{}].  \mforall{}[v:\mBbbZ{}].    uiff((g  *  v)  =  0;v  =  0)
Date html generated:
2019_06_20-AM-11_26_10
Last ObjectModification:
2018_10_15-PM-04_51_54
Theory : arithmetic
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