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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