Nuprl Lemma : sq_stable__monoid_hom_p
∀[a,b:GrpSig]. ∀[f:|a| ⟶ |b|]. SqStable(IsMonHom{a,b}(f))
Proof
Definitions occuring in Statement :
monoid_hom_p: IsMonHom{M1,M2}(f),
grp_car: |g|,
grp_sig: GrpSig,
sq_stable: SqStable(P),
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x]
Definitions unfolded in proof :
monoid_hom_p: IsMonHom{M1,M2}(f),
fun_thru_2op: FunThru2op(A;B;opa;opb;f),
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
infix_ap: x f y,
so_apply: x[s],
prop: ℙ,
implies: P ⇒ Q,
sq_stable: SqStable(P),
and: P ∧ Q
Lemmas referenced :
sq_stable__and,
uall_wf,
grp_car_wf,
equal_wf,
grp_op_wf,
grp_id_wf,
sq_stable__uall,
sq_stable__equal,
squash_wf,
and_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,
lambdaEquality,
applyEquality,
isect_memberEquality,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
axiomEquality,
lambdaFormation,
productElimination,
independent_pairEquality,
functionEquality
Latex:
\mforall{}[a,b:GrpSig]. \mforall{}[f:|a| {}\mrightarrow{} |b|]. SqStable(IsMonHom\{a,b\}(f))
Date html generated:
2016_05_15-PM-00_09_55
Last ObjectModification:
2015_12_26-PM-11_45_03
Theory : groups_1
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