test(tests/lean/run/sigma_no_confusion): define 'no_confusion' for sigma types

tests/lean/run/sigma_no_confusion.lean

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+import data.sigma tools.tactic
+
+namespace sigma
+  definition no_confusion_type {A : Type} {B : A → Type} (P : Type) (v₁ v₂ : sigma B) : Type :=
+  cases_on v₁
+    (λ (a₁ : A) (b₁ : B a₁), cases_on v₂
+      (λ (a₂ : A) (b₂ : B a₂),
+         (Π (eq₁ : a₁ = a₂), eq.rec_on eq₁ b₁ = b₂ → P) → P))
+
+  definition no_confusion {A : Type} {B : A → Type} {P : Type} {v₁ v₂ : sigma B} : v₁ = v₂ → no_confusion_type P v₁ v₂ :=
+  assume H₁₂ : v₁ = v₂,
+    have aux : v₁ = v₁ → no_confusion_type P v₁ v₁, from
+      assume H₁₁, cases_on v₁
+        (λ (a₁ : A) (b₁ : B a₁) (h : Π (eq₁ : a₁ = a₁), eq.rec_on eq₁ b₁ = b₁ → P),
+           h rfl rfl),
+    eq.rec_on H₁₂ aux H₁₂
+
+ theorem sigma.mk.inj_1 {A : Type} {B : A → Type} {a₁ a₂ : A} {b₁ : B a₁} {b₂ : B a₂} (Heq : dpair a₁ b₁ = dpair a₂ b₂) : a₁ = a₂ :=
+ begin
+   apply (no_confusion Heq), intros, assumption
+ end
+
+ theorem sigma.mk.inj_2 {A : Type} {B : A → Type} (a₁ a₂ : A) (b₁ : B a₁) (b₂ : B a₂) (Heq : dpair a₁ b₁ = dpair a₂ b₂) :
+   eq.rec_on (sigma.mk.inj_1 Heq) b₁ = b₂ :=
+ begin
+   apply (no_confusion Heq), intros, eassumption
+ end
+end sigma