Nuprl Lemma : id-is-monoid_hom
∀[A:GrpSig]. (λx.x ∈ MonHom(A,A))
Proof
Definitions occuring in Statement :
monoid_hom: MonHom(M1,M2),
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
member: t ∈ T,
lambda: λx.A[x]
Definitions unfolded in proof :
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
and: P ∧ Q,
monoid_hom_p: IsMonHom{M1,M2}(f),
prop: ℙ,
member: t ∈ T,
uall: ∀[x:A]. B[x],
monoid_hom: MonHom(M1,M2)
Lemmas referenced :
grp_id_wf,
grp_op_wf,
infix_ap_wf,
grp_sig_wf,
monoid_hom_p_wf,
grp_car_wf
Rules used in proof :
isect_memberEquality,
because_Cache,
independent_pairFormation,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
applyEquality,
functionExtensionality,
hypothesis,
thin,
isectElimination,
sqequalHypSubstitution,
extract_by_obid,
hypothesisEquality,
lambdaEquality,
dependent_set_memberEquality,
cut,
introduction,
isect_memberFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}[A:GrpSig]. (\mlambda{}x.x \mmember{} MonHom(A,A))
Date html generated:
2017_01_19-PM-02_30_35
Last ObjectModification:
2017_01_16-PM-01_02_27
Theory : groups_1
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