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: equal: t ∈ T
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] member: t ∈ T uiff: uiff(P;Q) and: P ∧ Q uimplies: supposing a all: x:A. B[x] le: A ≤ B not: ¬A implies:  Q false: False prop:
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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