21 lines
810 B
Text
21 lines
810 B
Text
prelude
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import init.meta init.logic init.data.nat.lemmas
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import init.data.char.basic
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namespace char
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lemma val_of_nat_eq_of_is_valid {n : nat} : is_valid_char n → (of_nat n).val = n :=
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by intro h; unfold of_nat; rw [dif_pos h]
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lemma val_of_nat_eq_of_not_is_valid {n : nat} : ¬ is_valid_char n → (of_nat n).val = 0 :=
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by intro h; unfold of_nat; rw [dif_neg h]
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lemma of_nat_eq_of_not_is_valid {n : nat} : ¬ is_valid_char n → of_nat n = of_nat 0 :=
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by intro h; apply eq_of_veq; rw [val_of_nat_eq_of_not_is_valid h]; reflexivity
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lemma of_nat_ne_of_ne {n₁ n₂ : nat} (h₁ : n₁ ≠ n₂) (h₂ : is_valid_char n₁) (h₃ : is_valid_char n₂) : of_nat n₁ ≠ of_nat n₂ :=
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begin
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apply ne_of_vne,
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rw [val_of_nat_eq_of_is_valid h₂, val_of_nat_eq_of_is_valid h₃],
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assumption
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end
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end char
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