35 lines
665 B
Text
35 lines
665 B
Text
new_frontend
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theorem tst0 (x : Nat) : x + 0 = x + 0 :=
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begin
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generalize x + 0 = y;
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exact (Eq.refl y)
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end
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theorem tst1 (x : Nat) : x + 0 = x + 0 :=
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begin
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generalize h : x + 0 = y;
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exact (Eq.refl y)
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end
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theorem tst2 (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y :=
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begin
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generalize h' : x + x = z;
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subst y;
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exact Eq.refl $ z + w
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end
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theorem tst3 (x y w : Nat) (h : x + x = y) : (x + x) + (x+x) = (x + x) + y :=
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begin
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generalize h' : x + x = z;
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subst z;
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subst y;
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exact rfl
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end
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theorem tst4 (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y :=
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begin
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generalize h' : x + y = z; -- just add equality
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subst h;
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exact rfl
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end
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