Nuprl Lemma : massoc_equiv_rel
∀g:IAbMonoid. EquivRel(|g|;x,y.x ~ y)
Proof
Definitions occuring in Statement :
massoc: a ~ b,
equiv_rel: EquivRel(T;x,y.E[x; y]),
all: ∀x:A. B[x],
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
massoc: a ~ b,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
implies: P ⇒ Q
Lemmas referenced :
iabmonoid_wf,
symmetrized_preorder,
grp_car_wf,
mdivides_wf,
mdivides_preorder
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
sqequalRule,
cut,
lemma_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
lambdaEquality,
dependent_functionElimination,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. EquivRel(|g|;x,y.x \msim{} y)
Date html generated:
2016_05_16-AM-07_43_25
Last ObjectModification:
2015_12_28-PM-05_54_25
Theory : factor_1
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