Nuprl Lemma : massoc_weakening
∀g:IAbMonoid. ∀a,b:|g|. ((a = b ∈ |g|) ⇒ (a ~ b))
Proof
Definitions occuring in Statement :
massoc: a ~ b,
all: ∀x:A. B[x],
implies: P ⇒ Q,
equal: s = t ∈ T,
iabmonoid: IAbMonoid,
grp_car: |g|
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
uall: ∀[x:A]. B[x],
iabmonoid: IAbMonoid,
imon: IMonoid,
equiv_rel: EquivRel(T;x,y.E[x; y]),
and: P ∧ Q,
refl: Refl(T;x,y.E[x; y])
Lemmas referenced :
equal_wf,
grp_car_wf,
iabmonoid_wf,
massoc_equiv_rel,
massoc_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
productElimination,
hyp_replacement,
equalitySymmetry,
applyLambdaEquality,
sqequalRule
Latex:
\mforall{}g:IAbMonoid. \mforall{}a,b:|g|. ((a = b) {}\mRightarrow{} (a \msim{} b))
Date html generated:
2017_01_09-AM-08_38_29
Last ObjectModification:
2016_07_12-PM-01_12_35
Theory : factor_1
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