Nuprl Lemma : inj_mon_hom_properties
∀[g,h:GrpSig]. ∀[f:InjMonHom(g;h)]. Inj(|g|;|h|;f)
Proof
Definitions occuring in Statement :
inj_mon_hom: InjMonHom(g;h)
,
grp_car: |g|
,
grp_sig: GrpSig
,
inject: Inj(A;B;f)
,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
inj_mon_hom: InjMonHom(g;h)
,
monoid_hom: MonHom(M1,M2)
,
sq_stable: SqStable(P)
,
implies: P
⇒ Q
,
squash: ↓T
,
inject: Inj(A;B;f)
,
all: ∀x:A. B[x]
,
prop: ℙ
Lemmas referenced :
sq_stable__inject,
grp_car_wf,
equal_wf,
inj_mon_hom_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
extract_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
independent_functionElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
lambdaEquality,
dependent_functionElimination,
axiomEquality,
applyEquality,
because_Cache,
isect_memberEquality
Latex:
\mforall{}[g,h:GrpSig]. \mforall{}[f:InjMonHom(g;h)]. Inj(|g|;|h|;f)
Date html generated:
2017_10_01-AM-08_14_06
Last ObjectModification:
2017_02_28-PM-01_58_12
Theory : groups_1
Home
Index