Nuprl Lemma : mon_hom_inj_p_wf
∀[g,h:GrpSig]. ∀[f:|g| ⟶ |h|]. (IsMonHomInj(g;h;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
mon_hom_inj_p: IsMonHomInj(g;h;f),
grp_car: |g|,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
mon_hom_inj_p: IsMonHomInj(g;h;f),
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
and_wf,
monoid_hom_p_wf,
inject_wf,
grp_car_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g,h:GrpSig]. \mforall{}[f:|g| {}\mrightarrow{} |h|]. (IsMonHomInj(g;h;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_09_49
Last ObjectModification:
2015_12_26-PM-11_45_05
Theory : groups_1
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