Nuprl Lemma : mul-distributes-right
∀[x:ℤ]. ∀[y,z:Top]. ((y + z) * x ~ (y * x) + (z * x))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
add: n + m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
top_wf,
mul-distributes,
mul-commutes
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesis,
sqequalAxiom,
lemma_by_obid,
sqequalRule,
sqequalHypSubstitution,
isect_memberEquality,
isectElimination,
thin,
hypothesisEquality,
because_Cache,
intEquality,
voidElimination,
voidEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y,z:Top]. ((y + z) * x \msim{} (y * x) + (z * x))
Date html generated:
2016_05_13-PM-03_29_10
Last ObjectModification:
2015_12_26-AM-09_48_08
Theory : arithmetic
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