30 lines
671 B
Text
30 lines
671 B
Text
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example (x : Nat) : x + 0 = x + 0 := by
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generalize x + 0 = y
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rfl
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example (x : Nat) : x + 0 = x + 0 := by
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generalize h : x + 0 = y
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rfl
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example (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y := by
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generalize h' : x + x = z
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subst y
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rfl
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example (x y w : Nat) (h : x + x = y) : (x + x) + (x+x) = (x + x) + y := by
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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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rfl
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example (x y w : Nat) (h : y = w) : (x + x) + w = (x + x) + y := by
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generalize h' : x + y = z -- just add equality
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subst h
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rfl
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example (x y w : Nat) (h : y = w) (H : (x + x) + w = (x + x) + y) :
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(x + x) + w = (x + x) + y := by
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generalize h' : x + x = z at H
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exact H
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