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
Lemmas :
sq_stable__le,
decidable__le,
decidable__lt,
false_wf,
not-le-2,
condition-implies-le,
minus-add,
minus-zero,
add-zero,
add-commutes,
zero-add,
add_functionality_wrt_le,
le-add-cancel,
bm_compare_greater_greater_false,
trans_wf,
le_wf,
anti_sym_wf,
connex_wf,
refl_wf,
equal-wf-T-base,
sym_wf,
less_than_wf,
bm_compare_wf
\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:
2015_07_17-AM-08_19_33
Last ObjectModification:
2015_01_27-PM-00_37_00
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