Nuprl Lemma : bm_compare_greater_greater_false
∀[K:Type]. ∀[compare:bm_compare(K)]. ∀[k1,k2:K]. (0 < compare k1 k2 ⇒ 0 < compare k2 k1 ⇒ 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,
bm_compare: bm_compare(K),
and: P ∧ Q,
anti_sym: AntiSym(T;x,y.R[x; y]),
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
not: ¬A,
top: Top,
prop: ℙ,
refl: Refl(T;x,y.E[x; y])
Latex:
\mforall{}[K:Type]. \mforall{}[compare:bm\_compare(K)]. \mforall{}[k1,k2:K]. (0 < compare k1 k2 {}\mRightarrow{} 0 < compare k2 k1 {}\mRightarrow{} False)
Date html generated:
2016_05_17-PM-01_40_56
Last ObjectModification:
2016_01_17-AM-11_20_13
Theory : binary-map
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