Nuprl Lemma : decidable__less_than'
∀i,j:ℤ. Dec(less_than'(i;j))
Proof
Definitions occuring in Statement :
less_than': less_than'(a;b),
decidable: Dec(P),
all: ∀x:A. B[x],
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
less_than': less_than'(a;b),
decidable: Dec(P),
not: ¬A,
or: P ∨ Q,
true: True,
implies: P ⇒ Q,
prop: ℙ,
false: False,
uall: ∀[x:A]. B[x]
Lemmas referenced :
true_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
lessCases,
hypothesisEquality,
intEquality,
thin,
baseClosed,
inlEquality,
sqequalRule,
axiomEquality,
natural_numberEquality,
functionEquality,
cut,
extract_by_obid,
sqequalHypSubstitution,
hypothesis,
inrEquality,
lambdaEquality,
voidElimination,
because_Cache,
isectElimination
Latex:
\mforall{}i,j:\mBbbZ{}. Dec(less\_than'(i;j))
Date html generated:
2019_06_20-AM-11_19_44
Last ObjectModification:
2018_08_04-PM-01_52_40
Theory : sqequal_1
Home
Index