Nuprl Lemma : div-mul-cancel2
∀[a:ℤ]. ∀[n,m:ℤ-o]. ((n * a) ÷ n * m ~ a ÷ m)
Proof
Definitions occuring in Statement :
int_nzero: ℤ-o,
uall: ∀[x:A]. B[x],
divide: n ÷ m,
multiply: n * m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
mul-commutes,
div-mul-cancel,
trivial-equal
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,
sqequalRule,
because_Cache,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
axiomSqEquality,
isect_memberEquality_alt,
hypothesisEquality,
isectIsTypeImplies,
inhabitedIsType
Latex:
\mforall{}[a:\mBbbZ{}]. \mforall{}[n,m:\mBbbZ{}\msupminus{}\msupzero{}]. ((n * a) \mdiv{} n * m \msim{} a \mdiv{} m)
Date html generated:
2020_05_19-PM-09_41_14
Last ObjectModification:
2019_12_28-AM-11_28_39
Theory : int_2
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