Nuprl Lemma : oal_le_wf
∀s:LOSet. ∀g:AbDGrp. ∀ps,qs:|oal(s;g)|. (ps ≤{s,g} qs ∈ ℙ1)
Proof
Definitions occuring in Statement :
oal_le: ps ≤{s,g} qs,
oalist: oal(a;b),
prop: ℙ,
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_le: ps ≤{s,g} qs
Lemmas referenced :
assert_wf,
oal_ble_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,
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,
setEquality,
applyEquality,
hypothesis,
hypothesisEquality,
dependent_functionElimination,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
instantiate,
thin,
cut,
lambdaFormation,
computationStep,
sqequalTransitivity,
sqequalReflexivity,
sqequalRule,
sqequalSubstitution
Latex:
\mforall{}s:LOSet. \mforall{}g:AbDGrp. \mforall{}ps,qs:|oal(s;g)|. (ps \mleq{}\{s,g\} qs \mmember{} \mBbbP{}\msubone{})
Date html generated:
2016_05_16-AM-08_20_41
Last ObjectModification:
2016_01_16-PM-11_56_34
Theory : polynom_2
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