Nuprl Lemma : bm_compare_less_to_greater_eq
∀[K:Type]. ∀[compare:bm_compare(K)]. ∀[k1,k2:K]. (compare k1 k2 < 0 ⇒ (0 ≤ (compare k2 k1)))
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,
connex: Connex(T;x,y.R[x; y]),
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
squash: ↓T
Latex:
\mforall{}[K:Type]. \mforall{}[compare:bm\_compare(K)]. \mforall{}[k1,k2:K]. (compare k1 k2 < 0 {}\mRightarrow{} (0 \mleq{} (compare k2 k1)))
Date html generated:
2016_05_17-PM-01_41_02
Last ObjectModification:
2016_01_17-AM-11_20_17
Theory : binary-map
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