Nuprl Lemma : zero_ann_a
∀[a,b:ℤ]. (a * b) = 0 ∈ ℤ supposing (a = 0 ∈ ℤ) ∨ (b = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
multiply: n * m,
natural_number: $n,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
or: P ∨ Q,
prop: ℙ,
subtype_rel: A ⊆r B,
top: Top
Lemmas referenced :
zero-mul,
equal-wf-base,
int_subtype_base,
mul-commutes,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
unionElimination,
thin,
hypothesis,
sqequalRule,
extract_by_obid,
isectElimination,
hypothesisEquality,
natural_numberEquality,
hyp_replacement,
equalitySymmetry,
Error :applyLambdaEquality,
because_Cache,
baseApply,
closedConclusion,
baseClosed,
applyEquality,
lambdaEquality,
isect_memberEquality,
voidElimination,
voidEquality,
intEquality,
axiomEquality,
equalityTransitivity
Latex:
\mforall{}[a,b:\mBbbZ{}]. (a * b) = 0 supposing (a = 0) \mvee{} (b = 0)
Date html generated:
2016_10_21-AM-09_37_22
Last ObjectModification:
2016_07_12-AM-05_00_40
Theory : arithmetic
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