diff options
Diffstat (limited to 'src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda')
| -rw-r--r-- | src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda | 5 |
1 files changed, 4 insertions, 1 deletions
diff --git a/src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda index eff2d37..db070e0 100644 --- a/src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda +++ b/src/Helium/Algebra/Ordered/StrictTotal/Properties/Ring.agda @@ -365,8 +365,11 @@ x≤0∧y≤0⇒x*y≥0 {x} {y} (inj₂ x≈0) y≤0 = ≤-reflexive (Eq. y * 1# ≈⟨ *-identityʳ y ⟩ y ∎ +x≉y⇒0<1 : ∀ {x y} → x ≉ y → 0# < 1# +x≉y⇒0<1 x≉y = ≤∧≉⇒< 0≤1 (x≉y ∘ 1≈0⇒x≈y ∘ Eq.sym) + x<y⇒0<1 : ∀ {x y} → x < y → 0# < 1# -x<y⇒0<1 x<y = ≤∧≉⇒< 0≤1 (<⇒≉ x<y ∘ 1≈0⇒x≈y ∘ Eq.sym) +x<y⇒0<1 = x≉y⇒0<1 ∘ <⇒≉ -------------------------------------------------------------------------------- ---- Properties of _*_ (again) |