Mathlib Map

Theorems · Theorem · number theory

Rat.pos

∀ (a : ℚ), 0 < a.den
Defined in
Mathlib.Data.Rat.Defs
Cited by
17 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Rat.cast_mul · cited by 19Rat.cast_mulRat.cast_add · cited by 19Rat.cast_addRat.cast_sub · cited by 9Rat.cast_subRat.pnatDen · cited by 4Rat.pnatDenPell.exists_of_not_isSquare · cited by 3Pell.exists_of_not_isSqua…LiouvilleWith.add_rat · cited by 2LiouvilleWith.add_ratRat.add_num_den' · cited by 2Rat.add_num_den'eventually_residual_liouville · cited by 2eventually_residual_liouv…LiouvilleWith.mul_rat · cited by 2LiouvilleWith.mul_ratRat.den_le_and_le_num_le_of_sub_lt_one_div_den_sq · cited by 1Rat.den_le_and_le_num_le_…Rat.finite_rat_abs_sub_lt_one_div_den_sq · cited by 1Rat.finite_rat_abs_sub_lt…Rat.cast_pos_of_pos · cited by 1Rat.cast_pos_of_posReal.exists_rat_abs_sub_le_and_den_le · cited by 1Real.exists_rat_abs_sub_l…Real.exists_rat_abs_sub_lt_and_lt_of_irrational · cited by 1Real.exists_rat_abs_sub_l…Real.exists_rat_eq_convergent · cited by 1Real.exists_rat_eq_conver…Rat.posCITED BYCITES

Cites0

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Nothing in Mathlib beyond the foundations.

Cited by18

Results whose statement or proof uses this declaration.