57 lines
1.1 KiB
Text
57 lines
1.1 KiB
Text
theorem ex1 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
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by {
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clear y x;
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exact z
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}
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theorem ex2 (x : Nat) (y : { v // v > x }) (z : Nat) : Nat :=
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by {
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clear x y;
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exact z
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}
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theorem ex3 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
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by {
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have y = z from h₂.symm;
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apply Eq.trans;
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exact h₁;
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assumption
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}
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theorem ex4 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
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by {
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let h₃ : y = z := h₂.symm;
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apply Eq.trans;
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exact h₁;
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exact h₃
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}
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theorem ex5 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
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by {
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have h₃ : y = z := h₂.symm;
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apply Eq.trans;
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exact h₁;
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exact h₃
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}
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theorem ex6 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : id (x + 0 = z) :=
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by {
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show x = z;
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have h₃ : y = z := h₂.symm;
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apply Eq.trans;
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exact h₁;
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exact h₃
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}
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theorem ex7 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z := by
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have y = z by apply Eq.symm; assumption
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apply Eq.trans
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exact h₁
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assumption
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theorem ex8 (x y z : Nat) (h₁ : x = y) (h₂ : z = y) : x = z :=
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by apply Eq.trans h₁;
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have y = z by
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apply Eq.symm;
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assumption;
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exact this
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