Nuprl Lemma : le_antisymmetry_iff
∀[x,y:ℤ]. uiff(x = y ∈ ℤ;{(x ≤ y) ∧ (y ≤ x)})
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
guard: {T},
le: A ≤ B,
and: P ∧ Q,
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
le: A ≤ B,
not: ¬A,
implies: P ⇒ Q,
false: False,
prop: ℙ
Lemmas referenced :
le_weakening,
less_than'_wf,
equal_wf,
le_antisymmetry,
and_wf,
le_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
hypothesis,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
independent_isectElimination,
equalitySymmetry,
productElimination,
independent_pairEquality,
lambdaEquality,
because_Cache,
isectElimination,
axiomEquality,
intEquality,
independent_functionElimination,
isect_memberEquality,
equalityTransitivity,
voidElimination
Latex:
\mforall{}[x,y:\mBbbZ{}]. uiff(x = y;\{(x \mleq{} y) \mwedge{} (y \mleq{} x)\})
Date html generated:
2016_05_13-PM-03_30_47
Last ObjectModification:
2015_12_26-AM-09_46_32
Theory : arithmetic
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