Documentation

Mathlib.Data.Int.Cast.Field

Cast of integers into fields #

This file concerns the canonical homomorphism ℤ → F, where F is a field.

Main results #

theorem Int.cast_neg_natCast {R : Type u_1} [inst : DivisionRing R] (n : ) :
↑(-n) = -n

Auxiliary lemma for norm_cast to move the cast -↑n upwards to ↑-↑n.

(The restriction to DivisionRing is necessary, otherwise this would also apply in the case where R = ℤ and cause nontermination.)

@[simp]
theorem Int.cast_div {α : Type u_1} [inst : DivisionRing α] {m : } {n : } (n_dvd : n m) (n_nonzero : n 0) :
↑(m / n) = m / n