Theorems · Theorem · commutative algebra
pow_injective_of_not_isUnit
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {q : M},
¬IsUnit q → q ≠ 0 → Function.Injective fun n => q ^ n- Defined in
- Mathlib.Algebra.Prime.Lemmas
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- IsUnitstatement and proof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- CommMonoidWithZerostatement and proof · cited by 913
- pow_ne_zeroproof · cited by 208
- IsCancelMulZerostatement and proof · cited by 177
- dvd_reflproof · cited by 97
- dvd_powproof · cited by 8
- pow_mul_pow_subproof · cited by 5
- not_isUnit_of_not_isUnit_dvdproof · cited by 3
- Function.Injective.of_lt_imp_neproof · cited by 1
- DvdNotUnit.neproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- DivisorChain.element_of_chain_eq_pow_second_of_chainproof · cited by 1
- pow_inj_of_not_isUnitproof · cited by 1