Nuprl Lemma : grp_lt_wf
∀[g:GrpSig]. ∀[a,b:|g|]. (a < b ∈ ℙ)
Proof
Definitions occuring in Statement :
grp_lt: a < b,
grp_car: |g|,
grp_sig: GrpSig,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
grp_lt: a < b,
uall: ∀[x:A]. B[x],
member: t ∈ T,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t)
Lemmas referenced :
set_lt_wf,
oset_of_ocmon_wf0,
grp_car_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,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[g:GrpSig]. \mforall{}[a,b:|g|]. (a < b \mmember{} \mBbbP{})
Date html generated:
2016_05_15-PM-00_11_51
Last ObjectModification:
2015_12_26-PM-11_42_57
Theory : groups_1
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