Nuprl Lemma : mul-swap
∀[x:ℤ]. ∀[y,z:Top]. (x * y * z ~ y * x * z)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
top: Top,
multiply: n * m,
int: ℤ,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top
Lemmas referenced :
mul-associates,
mul-commutes,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesisEquality,
hypothesis,
sqequalAxiom,
because_Cache,
intEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y,z:Top]. (x * y * z \msim{} y * x * z)
Date html generated:
2016_05_13-PM-03_29_11
Last ObjectModification:
2015_12_26-AM-09_47_56
Theory : arithmetic
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