Nuprl Lemma : permr_massoc_functionality
∀g:IAbMonoid. ∀as,as',bs,bs':|g| List. (as ≡ bs upto ~ ⇒ as' ≡ bs' upto ~ ⇒ (as ≡ as' upto ~ ⇐⇒ bs ≡ bs' upto ~))
Proof
Definitions occuring in Statement :
permr_massoc: as ≡ bs upto ~,
list: T List,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
iabmonoid: IAbMonoid,
imon: IMonoid,
uall: ∀[x:A]. B[x],
permr_massoc: as ≡ bs upto ~,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2]
Lemmas referenced :
permr_massoc_wf,
list_wf,
grp_car_wf,
iabmonoid_wf,
permr_upto_functionality_wrt_permr_upto,
massoc_wf,
massoc_equiv_rel
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
sqequalRule,
lambdaEquality,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}as,as',bs,bs':|g| List.
(as \mequiv{} bs upto \msim{} {}\mRightarrow{} as' \mequiv{} bs' upto \msim{} {}\mRightarrow{} (as \mequiv{} as' upto \msim{} \mLeftarrow{}{}\mRightarrow{} bs \mequiv{} bs' upto \msim{}))
Date html generated:
2016_05_16-AM-07_44_44
Last ObjectModification:
2015_12_28-PM-05_53_48
Theory : factor_1
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