Nuprl Lemma : grp_leq_weakening_lt
∀[g:OMon]. ∀[a,b:|g|]. a ≤ b supposing a < b
Proof
Definitions occuring in Statement :
grp_lt: a < b,
grp_leq: a ≤ b,
omon: OMon,
grp_car: |g|,
uimplies: b supposing a,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
loset: LOSet,
poset: POSet{i},
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
set_leq: a ≤ b,
set_le: ≤b,
pi2: snd(t),
grp_lt: a < b,
grp_leq: a ≤ b,
uimplies: b supposing a,
infix_ap: x f y,
omon: OMon,
abmonoid: AbMon,
mon: Mon,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
set_leq_weakening_lt,
oset_of_ocmon_wf,
loset_wf,
assert_witness,
grp_le_wf,
grp_lt_wf,
grp_car_wf,
omon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
applyEquality,
lambdaEquality,
setElimination,
rename,
sqequalRule,
isect_memberEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:OMon]. \mforall{}[a,b:|g|]. a \mleq{} b supposing a < b
Date html generated:
2016_05_15-PM-00_12_21
Last ObjectModification:
2015_12_26-PM-11_42_37
Theory : groups_1
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