### 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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