Nuprl Lemma : massoc_transitivity
∀g:IAbMonoid. ∀a,b,c:|g|. ((a ~ b) ⇒ (b ~ c) ⇒ (a ~ c))
Proof
Definitions occuring in Statement :
massoc: a ~ b,
all: ∀x:A. B[x],
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],
equiv_rel: EquivRel(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
and: P ∧ Q,
guard: {T},
sym: Sym(T;x,y.E[x; y])
Lemmas referenced :
massoc_wf,
grp_car_wf,
iabmonoid_wf,
massoc_equiv_rel,
massoc_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
productElimination,
because_Cache,
independent_functionElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}a,b,c:|g|. ((a \msim{} b) {}\mRightarrow{} (b \msim{} c) {}\mRightarrow{} (a \msim{} c))
Date html generated:
2016_05_16-AM-07_43_32
Last ObjectModification:
2015_12_28-PM-05_54_40
Theory : factor_1
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