Nuprl Lemma : div-cancel2
∀[x:ℤ]. ∀[y:ℤ-o]. ((y * x) ÷ y ~ x)
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,
int_nzero: ℤ-o,
top: Top
Lemmas referenced :
mul-commutes,
div-cancel,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
hypothesis,
sqequalAxiom,
sqequalRule,
because_Cache,
intEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:\mBbbZ{}\msupminus{}\msupzero{}]. ((y * x) \mdiv{} y \msim{} x)
Date html generated:
2016_05_14-AM-07_24_14
Last ObjectModification:
2015_12_26-PM-01_29_35
Theory : int_2
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