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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