Nuprl Lemma : le_antisymmetry
∀[x,y:ℤ]. ((x ≤ y) ⇒ (y ≤ x) ⇒ (x = y ∈ ℤ))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
le: A ≤ B,
implies: P ⇒ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
all: ∀x:A. B[x],
or: P ∨ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
false: False
Lemmas referenced :
less-trichotomy,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
unionElimination,
hypothesis,
isectElimination,
sqequalRule,
lambdaEquality,
axiomEquality,
intEquality,
isect_memberEquality,
because_Cache,
imageElimination,
productElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[x,y:\mBbbZ{}]. ((x \mleq{} y) {}\mRightarrow{} (y \mleq{} x) {}\mRightarrow{} (x = y))
Date html generated:
2019_06_20-AM-11_22_40
Last ObjectModification:
2018_08_17-AM-11_26_10
Theory : arithmetic
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