`Compfiles/Imo1984P3.lean`

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2 declarations, 0 contain sorry, 0 declared as axioms

International Mathematical Olympiad 1984, Problem 3

In the plane two different points O and A are given. For each point X of the plane, other than O, denote by a(X) the measure of the angle between OA and OX in radians, counterclockwise from OA (0 ≤ a(X) < 2π). Let C(X) be the circle with center O and radius of length OX + a(X)/OX. Each point of the plane is colored by one of a finite number of colors. Prove that there exists a point Y for which a(Y) > 0 such that its color appears on the circumference of the circle C(Y).

Imports (6)

Imported by 1 file

Compfiles.lean

def Imo1984P3.aang The angle a(X) from the problem statement: the measure in radians, counterclockwise from OA, of the angle between OA and OX, taking values in [0, 2 * π) line 36 source
Source documentation
The angle a(X) from the problem statement: the measure in radians, counterclockwise from OA, of the angle between OA and OX, taking values in [0, 2 * π). (The problem only uses this for X ≠ O; we define it for all X.)

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Complex, Real
Proof uses: ite, LE.le, OfNat.ofNat, Complex.arg, HDiv.hDiv, HSub.hSub, HAdd.hAdd, HMul.hMul, Real.pi
16 instances, coercions and auxiliary constants left out.
```
noncomputable def aang (O A X : ℂ) : ℝ :=
…
```
problem Imo1984P3.imo1984_p3 line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Fintype, Complex, Ne, Exists, And, LT.lt, Real, OfNat.ofNat, Imo1984P3.aang, Eq, Norm.norm, HSub.hSub, HAdd.hAdd, HDiv.hDiv
Proof uses: Decidable.byContradiction, Classical.propDecidable, Not, sub_ne_zero_of_ne, Ne.symm, Iff.mpr, norm_pos_iff, LT.lt.ne', Finset, Finset.filter, Finset.univ, rfl, Iff, Membership.mem, of_eq_true, Eq.trans, True, congrFun', congrArg, true_and and 132 more
196 instances, coercions and auxiliary constants left out.

Tactic trace: 105 steps
Open to load the checked before-and-after goal states.