Nuprl Lemma : div-cancel
∀[x:ℤ]. ∀[y:ℤ-o]. ((x * y) ÷ 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,
uimplies: b supposing a,
top: Top,
sq_type: SQType(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
guard: {T}
Lemmas referenced :
subtype_base_sq,
int_subtype_base,
mul-commutes,
divide-exact,
int_nzero_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
because_Cache,
independent_isectElimination,
hypothesis,
sqequalRule,
hypothesisEquality,
isect_memberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
sqequalAxiom,
intEquality
Latex:
\mforall{}[x:\mBbbZ{}]. \mforall{}[y:\mBbbZ{}\msupminus{}\msupzero{}]. ((x * y) \mdiv{} y \msim{} x)
Date html generated:
2016_05_14-AM-07_24_10
Last ObjectModification:
2015_12_26-PM-01_29_41
Theory : int_2
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