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
Home
Index