Nuprl Lemma : munit_char
∀g:IAbMonoid. ∀a:|g|. (g-unit(a) ⇐⇒ a ~ e)
Proof
Definitions occuring in Statement :
massoc: a ~ b,
munit: g-unit(u),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
iabmonoid: IAbMonoid,
grp_id: e,
grp_car: |g|
Definitions unfolded in proof :
munit: g-unit(u),
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
iabmonoid: IAbMonoid,
imon: IMonoid,
uall: ∀[x:A]. B[x],
rev_implies: P ⇐ Q,
massoc: a ~ b,
symmetrize: Symmetrize(x,y.R[x; y];a;b)
Lemmas referenced :
mdivides_wf,
grp_id_wf,
massoc_wf,
grp_car_wf,
iabmonoid_wf,
mdivides_id
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
lambdaFormation,
independent_pairFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
isectElimination,
because_Cache,
productElimination
Latex:
\mforall{}g:IAbMonoid. \mforall{}a:|g|. (g-unit(a) \mLeftarrow{}{}\mRightarrow{} a \msim{} e)
Date html generated:
2019_10_16-PM-01_05_45
Last ObjectModification:
2018_08_22-AM-09_39_30
Theory : factor_1
Home
Index