Nuprl Lemma : grp_lt_irreflexivity
∀[g:OCMon]. ∀[a:|g|].  False supposing a < a
Proof
Definitions occuring in Statement : 
grp_lt: a < b
, 
ocmon: OCMon
, 
grp_car: |g|
, 
uimplies: b supposing a
, 
uall: ∀[x:A]. B[x]
, 
false: False
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
subtype_rel: A ⊆r B
, 
ocmon: OCMon
, 
omon: OMon
, 
so_lambda: λ2x.t[x]
, 
prop: ℙ
, 
and: P ∧ Q
, 
abmonoid: AbMon
, 
mon: Mon
, 
so_lambda: λ2x y.t[x; y]
, 
so_apply: x[s1;s2]
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
uimplies: b supposing a
, 
bfalse: ff
, 
infix_ap: x f y
, 
so_apply: x[s]
, 
cand: A c∧ B
, 
oset_of_ocmon: g↓oset
, 
dset_of_mon: g↓set
, 
set_car: |p|
, 
pi1: fst(t)
, 
grp_lt: a < b
, 
false: False
Lemmas referenced : 
set_lt_irreflexivity, 
oset_of_ocmon_wf, 
subtype_rel_sets, 
abmonoid_wf, 
ulinorder_wf, 
grp_car_wf, 
assert_wf, 
infix_ap_wf, 
bool_wf, 
grp_le_wf, 
equal_wf, 
grp_eq_wf, 
eqtt_to_assert, 
cancel_wf, 
grp_op_wf, 
uall_wf, 
monot_wf, 
grp_lt_wf, 
ocmon_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
applyEquality, 
sqequalRule, 
instantiate, 
hypothesis, 
because_Cache, 
lambdaEquality, 
productEquality, 
setElimination, 
rename, 
cumulativity, 
universeEquality, 
functionEquality, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
productElimination, 
independent_isectElimination, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
setEquality, 
independent_pairFormation, 
isect_memberEquality, 
voidElimination
Latex:
\mforall{}[g:OCMon].  \mforall{}[a:|g|].    False  supposing  a  <  a
Date html generated:
2017_10_01-AM-08_14_41
Last ObjectModification:
2017_02_28-PM-01_59_55
Theory : groups_1
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