Documentation
Acmoi
.
Exercise1_8
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Imports
Init
Mathlib.Tactic
Mathlib.Algebra.Algebra.Basic
Mathlib.Algebra.Ring.Defs
Mathlib.Data.Int.ModEq
Mathlib.RingTheory.Coprime.Basic
Imported by
obvious_fact_1
helper_fact
helper_fact_2
Lemma_1_61
source
theorem
obvious_fact_1
(n :
ℤ
)
(h :
n
≥
1
)
(x :
ℤ
)
:
x
+
n
≠
x
source
theorem
helper_fact
{a :
ℤ
}
{b :
ℤ
}
{n :
ℤ
}
{x :
ℤ
}
{y :
ℤ
}
(h :
a
*
x
+
b
*
y
=
n
)
:
n
=
a
*
(
x
-
b
)
+
b
*
(
y
+
a
)
source
theorem
helper_fact_2
{a :
ℤ
}
{b :
ℤ
}
{n :
ℤ
}
{x :
ℤ
}
{y :
ℤ
}
(h :
a
≥
1
∧
b
≥
1
∧
a
*
x
+
b
*
y
=
n
∧
n
>
2
*
a
*
b
-
a
-
b
)
:
x
≥
b
∨
y
≥
a
source
theorem
Lemma_1_61
(a :
ℤ
)
(b :
ℤ
)
(n :
ℤ
)
(x :
ℤ
)
(y :
ℤ
)
(h_sol_xy :
a
*
x
+
b
*
y
=
n
)
(a_pos :
a
≥
1
)
(b_pos :
b
≥
1
)
(x_nneg :
x
≥
0
)
(y_nneg :
y
≥
0
)
(n_geq :
n
>
2
*
a
*
b
-
a
-
b
)
:
∃ (
x1
:
ℤ
) (
y1
:
ℤ
),
x1
≥
0
∧
y1
≥
0
∧
a
*
x1
+
b
*
y1
=
n
∧
(
x1
≠
x
∨
y1
≠
y
)