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
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