Theorems · Theorem · group theory

Submonoid.log_mul

∀ {M : Type u_1} [inst : Monoid M] [inst_1 : DecidableEq M] {n : M},
  (Function.Injective fun m => n ^ m) →
    ∀ (x y : ↥(Submonoid.powers n)), Submonoid.log (x * y) = Submonoid.log x + Submonoid.log y

Defined in: Mathlib.Algebra.Group.Submonoid.Membership
Cited by: 0 results in Mathlib
Foundations: Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Monoid DecidableEq

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Monoidstatement and proof · cited by 3,887
Submonoidstatement · cited by 3,086
map_mulproof · cited by 1,137
MulEquiv.symmproof · cited by 482
Submonoid.powersstatement and proof · cited by 408
Submonoid.logstatement · cited by 5
Submonoid.powLogEquivproof · cited by 4

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