Nuprl Lemma : less-trichotomy
∀a,b:ℤ.  (a < b ∨ b < a ∨ (a = b ∈ ℤ))
Proof
Definitions occuring in Statement : 
less_than: a < b
, 
all: ∀x:A. B[x]
, 
or: P ∨ Q
, 
int: ℤ
, 
equal: s = t ∈ T
Definitions unfolded in proof : 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
subtype_rel: A ⊆r B
, 
prop: ℙ
, 
squash: ↓T
, 
true: True
, 
cand: A c∧ B
, 
and: P ∧ Q
, 
less_than: a < b
, 
or: P ∨ Q
, 
less_than': less_than'(a;b)
, 
uall: ∀[x:A]. B[x]
, 
guard: {T}
Lemmas referenced : 
int_subtype_base, 
equal-wf-base, 
less_than_wf, 
or_wf
Rules used in proof : 
intEquality, 
hypothesisEquality, 
lessCases, 
lambdaFormation, 
sqequalReflexivity, 
computationStep, 
sqequalTransitivity, 
sqequalSubstitution, 
applyEquality, 
extract_by_obid, 
imageMemberEquality, 
sqequalRule, 
introduction, 
independent_pairFormation, 
natural_numberEquality, 
inlFormation, 
baseClosed, 
thin, 
isectElimination, 
sqequalHypSubstitution, 
hypothesis, 
cut, 
inrFormation, 
because_Cache, 
lessTrichotomy
Latex:
\mforall{}a,b:\mBbbZ{}.    (a  <  b  \mvee{}  b  <  a  \mvee{}  (a  =  b))
Date html generated:
2019_06_20-AM-11_19_46
Last ObjectModification:
2019_01_27-PM-05_50_26
Theory : sqequal_1
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