Nuprl Lemma : mul_mon_of_rng_wf
∀[r:RngSig]. (r↓xmn ∈ GrpSig)
Proof
Definitions occuring in Statement :
mul_mon_of_rng: r↓xmn,
rng_sig: RngSig,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
mul_mon_of_rng: r↓xmn,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
member: t ∈ T
Lemmas referenced :
rng_car_wf,
rng_eq_wf,
rng_le_wf,
rng_times_wf,
rng_one_wf,
bool_wf,
rng_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
dependent_pairEquality,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
because_Cache,
lambdaEquality,
functionEquality,
productEquality,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[r:RngSig]. (r\mdownarrow{}xmn \mmember{} GrpSig)
Date html generated:
2016_05_15-PM-00_21_01
Last ObjectModification:
2015_12_27-AM-00_02_35
Theory : rings_1
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