Theorems · Theorem · commutative algebra
one_add_one_eq_two
∀ {R : Type u_1} [inst : AddMonoidWithOne R], 1 + 1 = 2- Defined in
- Mathlib.Data.Nat.Cast.Defs
- Cited by
- 65 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext
- Assumes
- AddMonoidWithOne
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Nat.cast_oneproof · cited by 2,501
- Nat.cast_addproof · cited by 586
- AddMonoidWithOnestatement and proof · cited by 313
Cited by65
Results whose statement or proof uses this declaration.
- two_mulproof · cited by 232
- one_lt_twoproof · cited by 67
- two_smulproof · cited by 57
- one_le_twoproof · cited by 44
- zero_le_twoproof · cited by 44
- mul_twoproof · cited by 43
- even_twoproof · cited by 17
- Complex.continuous_expproof · cited by 8
- two_add_one_eq_threeproof · cited by 8
- Order.lt_two_iffproof · cited by 5
- Nat.sum_range_chooseproof · cited by 5
- Ring.neg_one_ne_one_of_char_ne_twoproof · cited by 5