Nuprl Lemma : monoid_hom_properties
∀[g,h:GrpSig]. ∀[f:MonHom(g,h)]. IsMonHom{g,h}(f)
Proof
Definitions occuring in Statement :
monoid_hom: MonHom(M1,M2),
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_sig: GrpSig,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
monoid_hom: MonHom(M1,M2),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
and: P ∧ Q,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
squash: ↓T
Lemmas referenced :
sq_stable__and,
uall_wf,
grp_car_wf,
equal_wf,
grp_op_wf,
infix_ap_wf,
sq_stable__uall,
sq_stable__equal,
squash_wf,
grp_id_wf,
set_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
setElimination,
thin,
rename,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
productElimination,
hypothesisEquality,
hypothesis,
lambdaEquality,
applyEquality,
functionExtensionality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
independent_functionElimination,
dependent_functionElimination,
axiomEquality,
lambdaFormation,
imageMemberEquality,
baseClosed,
imageElimination,
independent_pairEquality,
functionEquality,
productEquality
Latex:
\mforall{}[g,h:GrpSig]. \mforall{}[f:MonHom(g,h)]. IsMonHom\{g,h\}(f)
Date html generated:
2017_10_01-AM-08_13_58
Last ObjectModification:
2017_02_28-PM-01_58_22
Theory : groups_1
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