36 lines
950 B
Text
36 lines
950 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 of_nat_eq_of_lt {n : nat} : ∀ h : n < char_sz, of_nat n = fin.mk n h :=
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begin
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intro h,
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unfold of_nat,
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cases (nat.decidable_lt n char_sz),
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{contradiction},
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{reflexivity}
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end
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lemma of_nat_eq_fin_of_ge {n : nat} : n ≥ char_sz → of_nat n = fin.mk 0 zero_lt_char_sz :=
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begin
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intro h,
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unfold of_nat,
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cases (nat.decidable_lt n char_sz),
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{reflexivity},
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{have h' := not_lt_of_ge h, contradiction}
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end
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lemma of_nat_eq_of_ge {n : nat} : n ≥ char_sz → of_nat n = of_nat 0 :=
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begin
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intro h,
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rw [of_nat_eq_fin_of_ge h],
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reflexivity
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end
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lemma of_nat_ne_of_ne {n₁ n₂ : nat} (h₁ : n₁ ≠ n₂) (h₂ : n₁ < char_sz) (h₃ : n₂ < char_sz) : of_nat n₁ ≠ of_nat n₂ :=
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begin
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rw [of_nat_eq_of_lt h₂, of_nat_eq_of_lt h₃],
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apply @fin.ne_of_vne _ (fin.mk n₁ h₂) (fin.mk n₂ h₃) h₁
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end
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end char
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