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[Merged by Bors] - feat(algebra/char_zero): add char_zero lemma for ordered_semirings #6038

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[Merged by Bors] - feat(algebra/char_zero): add char_zero lemma for ordered_semirings #6038

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29c7b42
add characteristic zero lemma for ordered semirings
adomani Feb 4, 2021
060f0aa
Eric's suggestions
adomani Feb 4, 2021
b780518
lint
adomani Feb 4, 2021
b896bf2
Update src/algebra/char_zero.lean
adomani Feb 5, 2021
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8 changes: 7 additions & 1 deletion src/algebra/char_zero.lean
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Expand Up @@ -48,10 +48,16 @@ theorem char_zero_of_inj_zero {R : Type*} [add_left_cancel_monoid R] [has_one R]
rw [H k h, add_zero]
end⟩

/-- Note this is not an instances as `char_zero` implies `nontrivial`,
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and this would risk forming a loop. -/
lemma ordered_semiring.to_char_zero {R : Type*} [ordered_semiring R] [nontrivial R] :
char_zero R :=
⟨nat.strict_mono_cast.injective⟩

@[priority 100] -- see Note [lower instance priority]
instance linear_ordered_semiring.to_char_zero {R : Type*}
[linear_ordered_semiring R] : char_zero R :=
⟨nat.strict_mono_cast.injective⟩
ordered_semiring.to_char_zero

namespace nat
variables {R : Type*} [add_monoid R] [has_one R] [char_zero R]
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