Nuprl Lemma : oal_ble_wf
∀s:LOSet. ∀g:AbDGrp. ∀ps,qs:|oal(s;g)|. (ps ≤≤b qs ∈ 𝔹)
Proof
Definitions occuring in Statement :
oal_ble: ps ≤≤b qs
,
oalist: oal(a;b)
,
bool: 𝔹
,
all: ∀x:A. B[x]
,
member: t ∈ T
,
abdgrp: AbDGrp
,
loset: LOSet
,
set_car: |p|
Definitions unfolded in proof :
squash: ↓T
,
sq_stable: SqStable(P)
,
implies: P
⇒ Q
,
uimplies: b supposing a
,
so_apply: x[s]
,
so_lambda: λ2x.t[x]
,
prop: ℙ
,
mon: Mon
,
dmon: DMon
,
abdmonoid: AbDMon
,
grp: Group{i}
,
abgrp: AbGrp
,
abdgrp: AbDGrp
,
subtype_rel: A ⊆r B
,
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
all: ∀x:A. B[x]
,
oal_ble: ps ≤≤b qs
Lemmas referenced :
bor_wf,
infix_ap_wf,
set_car_wf,
oalist_wf,
subtype_rel_sets,
mon_wf,
inverse_wf,
grp_car_wf,
grp_op_wf,
grp_id_wf,
grp_inv_wf,
comm_wf,
eqfun_p_wf,
grp_eq_wf,
set_wf,
sq_stable__comm,
bool_wf,
set_eq_wf,
oal_blt_wf,
abdgrp_wf,
loset_wf
Rules used in proof :
imageElimination,
baseClosed,
imageMemberEquality,
introduction,
independent_functionElimination,
dependent_set_memberEquality,
independent_isectElimination,
universeEquality,
because_Cache,
lambdaEquality,
rename,
setElimination,
cumulativity,
hypothesis,
setEquality,
instantiate,
applyEquality,
hypothesisEquality,
dependent_functionElimination,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
cut,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDGrp. \mforall{}ps,qs:|oal(s;g)|. (ps \mleq{}\mleq{}\msubb{} qs \mmember{} \mBbbB{})
Date html generated:
2016_05_16-AM-08_20_36
Last ObjectModification:
2016_01_16-PM-11_56_39
Theory : polynom_2
Home
Index