Nuprl Lemma : less_than_irreflexivity
∀[x:ℤ]. (x < x ⇒ False)
Proof
Definitions occuring in Statement :
less_than: a < b,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
false: False,
int: ℤ
Definitions unfolded in proof :
prop: ℙ,
false: False,
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
or: P ∨ Q,
all: ∀x:A. B[x],
and: P ∧ Q,
less_than': less_than'(a;b),
squash: ↓T,
less_than: a < b
Lemmas referenced :
less_than_wf,
add-monotonic,
add-inverse
Rules used in proof :
intEquality,
voidElimination,
dependent_functionElimination,
lambdaEquality,
sqequalRule,
hypothesisEquality,
thin,
isectElimination,
sqequalHypSubstitution,
lemma_by_obid,
hypothesis,
lambdaFormation,
cut,
introduction,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
minusEquality,
inlFormation,
because_Cache,
extract_by_obid,
independent_functionElimination,
productElimination,
imageElimination
Latex:
\mforall{}[x:\mBbbZ{}]. (x < x {}\mRightarrow{} False)
Date html generated:
2019_06_20-AM-11_22_42
Last ObjectModification:
2018_08_17-AM-11_58_12
Theory : arithmetic
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