Nuprl Lemma : cons_functionality_wrt_permr_massoc
∀g:IAbMonoid. ∀a,b:|g|. ∀as,bs:|g| List. ((a ~ b) ⇒ as ≡ bs upto ~ ⇒ [a / as] ≡ [b / bs] upto ~)
Proof
Definitions occuring in Statement :
permr_massoc: as ≡ bs upto ~,
massoc: a ~ b,
cons: [a / b],
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 :
cons_functionality_wrt_permr_upto,
grp_car_wf,
massoc_wf,
massoc_equiv_rel,
permr_upto_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{}a,b:|g|. \mforall{}as,bs:|g| List. ((a \msim{} b) {}\mRightarrow{} as \mequiv{} bs upto \msim{} {}\mRightarrow{} [a / as] \mequiv{} [b / bs] upto \msim{})
Date html generated:
2016_05_16-AM-07_44_46
Last ObjectModification:
2015_12_28-PM-05_53_42
Theory : factor_1
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