Nuprl Lemma : assert_of_grp_blt
∀[g:OCMon]. ∀[a,b:|g|]. uiff(↑(a <b b);a < b)
Proof
Definitions occuring in Statement :
grp_blt: a <b b,
grp_lt: a < b,
ocmon: OCMon,
grp_car: |g|,
assert: ↑b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
ocmon: OCMon,
abmonoid: AbMon,
mon: Mon,
oset_of_ocmon: g↓oset,
dset_of_mon: g↓set,
set_car: |p|,
pi1: fst(t),
grp_blt: a <b b,
grp_lt: a < b,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
set_lt: a <p b,
implies: P ⇒ Q,
prop: ℙ
Lemmas referenced :
assert_of_set_lt,
oset_of_ocmon_wf0,
assert_witness,
set_blt_wf,
assert_wf,
grp_blt_wf,
grp_lt_wf,
grp_car_wf,
ocmon_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
sqequalRule,
isect_memberEquality,
productElimination,
independent_pairEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[g:OCMon]. \mforall{}[a,b:|g|]. uiff(\muparrow{}(a <\msubb{} b);a < b)
Date html generated:
2016_05_15-PM-00_13_34
Last ObjectModification:
2015_12_26-PM-11_41_30
Theory : groups_1
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