Theorems · Theorem · field theory
add_div_eq_mul_add_div
∀ {K : Type u_1} [inst : DivisionSemiring K] {c : K} (a b : K), c ≠ 0 → a + b / c = (a * c + b) / c- Defined in
- Mathlib.Algebra.Field.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DivisionSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DivisionSemiringstatement and proof · cited by 216
- div_mul_cancel₀proof · cited by 122
- right_distribproof · cited by 26
- eq_div_iff_mul_eqproof · cited by 19
Cited by3
Results whose statement or proof uses this declaration.
- Real.sqrtTwoAddSeries_step_downproof · cited by 5
- Real.sqrtTwoAddSeries_step_upproof · cited by 5
- liouvilleWith_oneproof · cited by 0