Nuprl Lemma : permr_massoc_weakening
∀g:IAbMonoid. ∀as,bs:|g| List. ((as ≡(|g|) bs) ⇒ as ≡ bs upto ~)
Proof
Definitions occuring in Statement :
permr_massoc: as ≡ bs upto ~,
permr: as ≡(T) bs,
list: T List,
all: ∀x:A. B[x],
implies: P ⇒ Q,
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
permr_massoc: as ≡ bs upto ~,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
prop: ℙ
Lemmas referenced :
permr_upto_weakening,
grp_car_wf,
massoc_wf,
massoc_equiv_rel,
permr_wf,
list_wf,
iabmonoid_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
isectElimination,
setElimination,
rename,
hypothesisEquality,
hypothesis,
lambdaEquality,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}as,bs:|g| List. ((as \mequiv{}(|g|) bs) {}\mRightarrow{} as \mequiv{} bs upto \msim{})
Date html generated:
2016_05_16-AM-07_44_41
Last ObjectModification:
2015_12_28-PM-05_53_36
Theory : factor_1
Home
Index