### Nuprl Lemma : comparison-anti

`∀[T:Type]. ∀[cmp:comparison(T)]. ∀[x,y:T].  ((cmp x y) = (-(cmp y x)) ∈ ℤ)`

Proof

Definitions occuring in Statement :  comparison: `comparison(T)` uall: `∀[x:A]. B[x]` apply: `f a` minus: `-n` int: `ℤ` universe: `Type` equal: `s = t ∈ T`
Definitions unfolded in proof :  uall: `∀[x:A]. B[x]` member: `t ∈ T` comparison: `comparison(T)` and: `P ∧ Q` squash: `↓T` prop: `ℙ` all: `∀x:A. B[x]` true: `True` subtype_rel: `A ⊆r B` uimplies: `b supposing a` guard: `{T}` iff: `P `⇐⇒` Q` rev_implies: `P `` Q` implies: `P `` Q`
Lemmas referenced :  equal_wf squash_wf true_wf iff_weakening_equal comparison_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity isect_memberFormation introduction cut sqequalHypSubstitution setElimination thin rename productElimination applyEquality lambdaEquality imageElimination extract_by_obid isectElimination hypothesisEquality equalityTransitivity hypothesis equalitySymmetry because_Cache intEquality dependent_functionElimination minusEquality functionExtensionality cumulativity natural_numberEquality sqequalRule imageMemberEquality baseClosed universeEquality independent_isectElimination independent_functionElimination isect_memberEquality axiomEquality

Latex:
\mforall{}[T:Type].  \mforall{}[cmp:comparison(T)].  \mforall{}[x,y:T].    ((cmp  x  y)  =  (-(cmp  y  x)))

Date html generated: 2017_04_17-AM-08_26_35
Last ObjectModification: 2017_02_27-PM-04_47_37

Theory : list_1

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