`Compfiles/Imo1968P6.lean`

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3 declarations, 0 contain sorry, 0 declared as axioms

International Mathematical Olympiad 1968, Problem 6

For every natural number n, evaluate the sum ∑_{k=0}^{∞} [(n + 2^k) / 2^(k+1)] where [x] denotes the greatest integer less than or equal to x.

Imports (4)

Imported by 1 file

Compfiles.lean

lemma Imo1968P6.term_telescope Lemma for the telescoping term structure line 31 source
Source comment
Lemma for the telescoping term structure

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Eq, HDiv.hDiv, HAdd.hAdd, HPow.hPow, OfNat.ofNat, HSub.hSub
Proof uses: Eq.mpr, HMul.hMul, id, congrArg, pow_succ, Eq.symm, Nat.div_div_eq_div_mul, LT.lt, pow_pos, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false, Nat.add_div_right
43 instances, coercions and auxiliary constants left out.

Tactic trace: 8 steps
Open to load the checked before-and-after goal states.
```
lemma term_telescope (n k : ℕ) :
    (n + 2^k) / 2^(k+1) = n / 2^k - n / 2^(k+1) := by
…
```
determine Imo1968P6.n_ans The answer is n line 46 source
Source documentation
The answer is n. We pull this into a determine statement as required.

no axioms what this means
Statement uses: Nat
```
determine n_ans (n : ℕ) : ℕ := n
```
problem Imo1968P6.imo1968_p6 line 48 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Eq, tsum, HDiv.hDiv, HAdd.hAdd, HPow.hPow, OfNat.ofNat, SummationFilter.unconditional, Imo1968P6.n_ans
Proof uses: id, Finset.sum, Finset.range, tsum_eq_sum, Not, Membership.mem, Finset, Nat.div_eq_of_lt, Trans.trans, LT.lt, add_lt_add_left, LE.le, Nat.lt_two_pow_self, Nat.pow_lt_pow_right, Mathlib.Meta.NormNum.isNat_lt_true, Mathlib.Meta.NormNum.isNat_ofNat, Eq.refl, Bool, Bool.false, le_refl and 31 more
97 instances, coercions and auxiliary constants left out.

Tactic trace: 37 steps
Open to load the checked before-and-after goal states.