Nuprl Lemma : bm_compare_greater_to_less_eq
∀[K:Type]. ∀[compare:bm_compare(K)]. ∀[k1,k2:K]. (0 < compare k1 k2 ⇒ ((compare k2 k1) ≤ 0))
Proof
Definitions occuring in Statement :
bm_compare: bm_compare(K),
less_than: a < b,
uall: ∀[x:A]. B[x],
le: A ≤ B,
implies: P ⇒ Q,
apply: f a,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
implies: P ⇒ Q,
bm_compare: bm_compare(K),
sq_stable: SqStable(P),
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
cand: A c∧ B,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
squash: ↓T,
le: A ≤ B
Latex:
\mforall{}[K:Type]. \mforall{}[compare:bm\_compare(K)]. \mforall{}[k1,k2:K]. (0 < compare k1 k2 {}\mRightarrow{} ((compare k2 k1) \mleq{} 0))
Date html generated:
2016_05_17-PM-01_40_59
Last ObjectModification:
2016_01_17-AM-11_20_19
Theory : binary-map
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