Nuprl Lemma : bm_compare_less_less_false
∀[K:Type]. ∀[compare:bm_compare(K)]. ∀[k1,k2:K]. (compare k1 k2 < 0 ⇒ compare k2 k1 < 0 ⇒ False)
Proof
Definitions occuring in Statement :
bm_compare: bm_compare(K),
less_than: a < b,
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
false: False,
apply: f a,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
false: False,
le: A ≤ B,
and: P ∧ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
all: ∀x:A. B[x],
top: Top,
prop: ℙ,
bm_compare: bm_compare(K)
Latex:
\mforall{}[K:Type]. \mforall{}[compare:bm\_compare(K)]. \mforall{}[k1,k2:K]. (compare k1 k2 < 0 {}\mRightarrow{} compare k2 k1 < 0 {}\mRightarrow{} False)
Date html generated:
2016_05_17-PM-01_41_04
Last ObjectModification:
2016_01_17-AM-11_20_09
Theory : binary-map
Home
Index