59 lines
715 B
Text
59 lines
715 B
Text
inductive F2 : Type
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| O : F2
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| I : F2
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namespace F2
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definition add : F2 → F2 → F2
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| O O := O
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| O I := I
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| I O := I
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| I I := O
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infix + := F2.add
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end F2
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open F2 nat
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#reduce (1 : nat) + 1
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#reduce (1 : nat) + (1 : nat)
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example : true :=
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begin
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have H : (1 : nat) + (1 : nat) = 2,
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reflexivity,
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constructor
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end
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example : true :=
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begin
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have H : 1 + 1 = 2,
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reflexivity,
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constructor
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end
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example : true :=
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begin
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have H : (1:nat) + 1 = 2,
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reflexivity,
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constructor
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end
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example : true :=
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begin
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have H : I + O = I,
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reflexivity,
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constructor
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end
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example : true :=
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begin
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have H1 : I + O = I,
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reflexivity,
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have H2 : 1 + 0 = 1,
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reflexivity,
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have H3 : (1:int) + 0 = 1,
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reflexivity,
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constructor
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end
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