Nuprl Lemma : comparison-seq-zero-simple
∀[T:Type]. ∀[c1,c2:comparison(T)]. ∀[x,y:T].
uiff((comparison-seq(c1; c2) x y) = 0 ∈ ℤ;((c1 x y) = 0 ∈ ℤ) ∧ ((c2 x y) = 0 ∈ ℤ))
Proof
Definitions occuring in Statement :
comparison-seq: comparison-seq(c1; c2),
comparison: comparison(T),
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
apply: f a,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
comparison: comparison(T),
prop: ℙ,
uimplies: b supposing a,
all: ∀x:A. B[x]
Lemmas referenced :
comparison-seq-zero,
subtype_rel_comparison,
equal-wf-T-base,
comparison_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
applyEquality,
setEquality,
cumulativity,
intEquality,
setElimination,
rename,
baseClosed,
because_Cache,
independent_isectElimination,
lambdaEquality,
sqequalRule,
dependent_functionElimination,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[c1,c2:comparison(T)]. \mforall{}[x,y:T].
uiff((comparison-seq(c1; c2) x y) = 0;((c1 x y) = 0) \mwedge{} ((c2 x y) = 0))
Date html generated:
2017_04_17-AM-08_28_49
Last ObjectModification:
2017_02_27-PM-04_49_22
Theory : list_1
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