Nuprl Lemma : dset_of_mon_wf
∀[g:DMon]. (g↓set ∈ DSet)
Proof
Definitions occuring in Statement :
dset_of_mon: g↓set,
dmon: DMon,
dset: DSet,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
dset_of_mon: g↓set,
uall: ∀[x:A]. B[x],
member: t ∈ T,
dset: DSet,
poset_sig: PosetSig,
dmon: DMon,
mon: Mon,
set_car: |p|,
pi1: fst(t),
grp_car: |g|,
set_eq: =b,
pi2: snd(t),
grp_eq: =b,
prop: ℙ
Lemmas referenced :
dmon_wf,
dmon_properties,
grp_car_wf,
grp_eq_wf,
grp_le_wf,
bool_wf,
eqfun_p_wf,
set_car_wf,
set_eq_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
lemma_by_obid,
isectElimination,
thin,
hypothesisEquality,
dependent_set_memberEquality,
dependent_pairEquality,
setElimination,
rename,
functionEquality,
productEquality
Latex:
\mforall{}[g:DMon]. (g\mdownarrow{}set \mmember{} DSet)
Date html generated:
2016_05_15-PM-00_10_43
Last ObjectModification:
2015_12_26-PM-11_44_28
Theory : groups_1
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