Nuprl Lemma : mdivides_preorder
∀g:IAbMonoid. Preorder(|g|;x,y.x | y)
Proof
Definitions occuring in Statement :
mdivides: b | a,
preorder: Preorder(T;x,y.R[x; y]),
all: ∀x:A. B[x],
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
preorder: Preorder(T;x,y.R[x; y]),
trans: Trans(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
and: P ∧ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
grp_car_wf,
mdivides_wf,
iabmonoid_wf,
mdivides_refl,
mdivides_trans
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. Preorder(|g|;x,y.x | y)
Date html generated:
2016_05_16-AM-07_43_02
Last ObjectModification:
2015_12_28-PM-05_54_51
Theory : factor_1
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