web site update

[helm.git] / matita / matita / contribs / lambdadelta / ground_2 / xoa / xoa.ma

diff --git a/matita/matita/contribs/lambdadelta/ground_2/xoa/xoa.ma b/matita/matita/contribs/lambdadelta/ground_2/xoa/xoa.ma
index 4ff65068fb15bbd61937cd3cb8e1a6c96d824f7e..0a1113ca32ee8d0d89cea3fda41ccfcb10f51504 100644 (file)
--- a/matita/matita/contribs/lambdadelta/ground_2/xoa/xoa.ma
+++ b/matita/matita/contribs/lambdadelta/ground_2/xoa/xoa.ma
@@ -24,7 +24,7 @@ inductive ex1_2 (A0,A1:Type[0]) (P0:A0→A1→Prop) : Prop ≝
    | ex1_2_intro: ∀x0,x1. P0 x0 x1 → ex1_2 ? ? ?
 .
 
-interpretation "multiple existental quantifier (1, 2)" 'Ex P0 = (ex1_2 ? ? P0).
+interpretation "multiple existental quantifier (1, 2)" 'Ex2 P0 = (ex1_2 ? ? P0).
 
 (* multiple existental quantifier (1, 3) *)
 
@@ -32,7 +32,7 @@ inductive ex1_3 (A0,A1,A2:Type[0]) (P0:A0→A1→A2→Prop) : Prop ≝
    | ex1_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → ex1_3 ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (1, 3)" 'Ex P0 = (ex1_3 ? ? ? P0).
+interpretation "multiple existental quantifier (1, 3)" 'Ex3 P0 = (ex1_3 ? ? ? P0).
 
 (* multiple existental quantifier (2, 2) *)
 
@@ -40,7 +40,7 @@ inductive ex2_2 (A0,A1:Type[0]) (P0,P1:A0→A1→Prop) : Prop ≝
    | ex2_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → ex2_2 ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (2, 2)" 'Ex P0 P1 = (ex2_2 ? ? P0 P1).
+interpretation "multiple existental quantifier (2, 2)" 'Ex2 P0 P1 = (ex2_2 ? ? P0 P1).
 
 (* multiple existental quantifier (2, 3) *)
 
@@ -48,7 +48,7 @@ inductive ex2_3 (A0,A1,A2:Type[0]) (P0,P1:A0→A1→A2→Prop) : Prop ≝
    | ex2_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → ex2_3 ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (2, 3)" 'Ex P0 P1 = (ex2_3 ? ? ? P0 P1).
+interpretation "multiple existental quantifier (2, 3)" 'Ex3 P0 P1 = (ex2_3 ? ? ? P0 P1).
 
 (* multiple existental quantifier (3, 1) *)
 
@@ -64,7 +64,7 @@ inductive ex3_2 (A0,A1:Type[0]) (P0,P1,P2:A0→A1→Prop) : Prop ≝
    | ex3_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → ex3_2 ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (3, 2)" 'Ex P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
+interpretation "multiple existental quantifier (3, 2)" 'Ex2 P0 P1 P2 = (ex3_2 ? ? P0 P1 P2).
 
 (* multiple existental quantifier (3, 3) *)
 
@@ -72,7 +72,7 @@ inductive ex3_3 (A0,A1,A2:Type[0]) (P0,P1,P2:A0→A1→A2→Prop) : Prop ≝
    | ex3_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → ex3_3 ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (3, 3)" 'Ex P0 P1 P2 = (ex3_3 ? ? ? P0 P1 P2).
+interpretation "multiple existental quantifier (3, 3)" 'Ex3 P0 P1 P2 = (ex3_3 ? ? ? P0 P1 P2).
 
 (* multiple existental quantifier (3, 4) *)
 
@@ -80,7 +80,7 @@ inductive ex3_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2:A0→A1→A2→A3→Prop) : Prop
    | ex3_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → ex3_4 ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (3, 4)" 'Ex P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
+interpretation "multiple existental quantifier (3, 4)" 'Ex4 P0 P1 P2 = (ex3_4 ? ? ? ? P0 P1 P2).
 
 (* multiple existental quantifier (3, 5) *)
 
@@ -88,7 +88,7 @@ inductive ex3_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2:A0→A1→A2→A3→A4→Prop
    | ex3_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → ex3_5 ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (3, 5)" 'Ex P0 P1 P2 = (ex3_5 ? ? ? ? ? P0 P1 P2).
+interpretation "multiple existental quantifier (3, 5)" 'Ex5 P0 P1 P2 = (ex3_5 ? ? ? ? ? P0 P1 P2).
 
 (* multiple existental quantifier (4, 1) *)
 
@@ -104,7 +104,7 @@ inductive ex4_2 (A0,A1:Type[0]) (P0,P1,P2,P3:A0→A1→Prop) : Prop ≝
    | ex4_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → P3 x0 x1 → ex4_2 ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (4, 2)" 'Ex P0 P1 P2 P3 = (ex4_2 ? ? P0 P1 P2 P3).
+interpretation "multiple existental quantifier (4, 2)" 'Ex2 P0 P1 P2 P3 = (ex4_2 ? ? P0 P1 P2 P3).
 
 (* multiple existental quantifier (4, 3) *)
 
@@ -112,7 +112,7 @@ inductive ex4_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3:A0→A1→A2→Prop) : Prop ≝
    | ex4_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → ex4_3 ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (4, 3)" 'Ex P0 P1 P2 P3 = (ex4_3 ? ? ? P0 P1 P2 P3).
+interpretation "multiple existental quantifier (4, 3)" 'Ex3 P0 P1 P2 P3 = (ex4_3 ? ? ? P0 P1 P2 P3).
 
 (* multiple existental quantifier (4, 4) *)
 
@@ -120,7 +120,7 @@ inductive ex4_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3:A0→A1→A2→A3→Prop) : P
    | ex4_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → ex4_4 ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (4, 4)" 'Ex P0 P1 P2 P3 = (ex4_4 ? ? ? ? P0 P1 P2 P3).
+interpretation "multiple existental quantifier (4, 4)" 'Ex4 P0 P1 P2 P3 = (ex4_4 ? ? ? ? P0 P1 P2 P3).
 
 (* multiple existental quantifier (4, 5) *)
 
@@ -128,7 +128,7 @@ inductive ex4_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3:A0→A1→A2→A3→A4→P
    | ex4_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → P3 x0 x1 x2 x3 x4 → ex4_5 ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (4, 5)" 'Ex P0 P1 P2 P3 = (ex4_5 ? ? ? ? ? P0 P1 P2 P3).
+interpretation "multiple existental quantifier (4, 5)" 'Ex5 P0 P1 P2 P3 = (ex4_5 ? ? ? ? ? P0 P1 P2 P3).
 
 (* multiple existental quantifier (5, 2) *)
 
@@ -136,7 +136,7 @@ inductive ex5_2 (A0,A1:Type[0]) (P0,P1,P2,P3,P4:A0→A1→Prop) : Prop ≝
    | ex5_2_intro: ∀x0,x1. P0 x0 x1 → P1 x0 x1 → P2 x0 x1 → P3 x0 x1 → P4 x0 x1 → ex5_2 ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (5, 2)" 'Ex P0 P1 P2 P3 P4 = (ex5_2 ? ? P0 P1 P2 P3 P4).
+interpretation "multiple existental quantifier (5, 2)" 'Ex2 P0 P1 P2 P3 P4 = (ex5_2 ? ? P0 P1 P2 P3 P4).
 
 (* multiple existental quantifier (5, 3) *)
 
@@ -144,7 +144,7 @@ inductive ex5_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3,P4:A0→A1→A2→Prop) : Prop 
    | ex5_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → P4 x0 x1 x2 → ex5_3 ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (5, 3)" 'Ex P0 P1 P2 P3 P4 = (ex5_3 ? ? ? P0 P1 P2 P3 P4).
+interpretation "multiple existental quantifier (5, 3)" 'Ex3 P0 P1 P2 P3 P4 = (ex5_3 ? ? ? P0 P1 P2 P3 P4).
 
 (* multiple existental quantifier (5, 4) *)
 
@@ -152,7 +152,7 @@ inductive ex5_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4:A0→A1→A2→A3→Prop)
    | ex5_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → ex5_4 ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (5, 4)" 'Ex P0 P1 P2 P3 P4 = (ex5_4 ? ? ? ? P0 P1 P2 P3 P4).
+interpretation "multiple existental quantifier (5, 4)" 'Ex4 P0 P1 P2 P3 P4 = (ex5_4 ? ? ? ? P0 P1 P2 P3 P4).
 
 (* multiple existental quantifier (5, 5) *)
 
@@ -160,7 +160,7 @@ inductive ex5_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4:A0→A1→A2→A3→A4
    | ex5_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → ex5_5 ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (5, 5)" 'Ex P0 P1 P2 P3 P4 = (ex5_5 ? ? ? ? ? P0 P1 P2 P3 P4).
+interpretation "multiple existental quantifier (5, 5)" 'Ex5 P0 P1 P2 P3 P4 = (ex5_5 ? ? ? ? ? P0 P1 P2 P3 P4).
 
 (* multiple existental quantifier (5, 6) *)
 
@@ -168,7 +168,7 @@ inductive ex5_6 (A0,A1,A2,A3,A4,A5:Type[0]) (P0,P1,P2,P3,P4:A0→A1→A2→A3→
    | ex5_6_intro: ∀x0,x1,x2,x3,x4,x5. P0 x0 x1 x2 x3 x4 x5 → P1 x0 x1 x2 x3 x4 x5 → P2 x0 x1 x2 x3 x4 x5 → P3 x0 x1 x2 x3 x4 x5 → P4 x0 x1 x2 x3 x4 x5 → ex5_6 ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (5, 6)" 'Ex P0 P1 P2 P3 P4 = (ex5_6 ? ? ? ? ? ? P0 P1 P2 P3 P4).
+interpretation "multiple existental quantifier (5, 6)" 'Ex6 P0 P1 P2 P3 P4 = (ex5_6 ? ? ? ? ? ? P0 P1 P2 P3 P4).
 
 (* multiple existental quantifier (6, 3) *)
 
@@ -176,7 +176,7 @@ inductive ex6_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→Prop) : Pro
    | ex6_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → P4 x0 x1 x2 → P5 x0 x1 x2 → ex6_3 ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 3)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_3 ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 3)" 'Ex3 P0 P1 P2 P3 P4 P5 = (ex6_3 ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 4) *)
 
@@ -184,7 +184,7 @@ inductive ex6_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→A3→Pro
    | ex6_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → P5 x0 x1 x2 x3 → ex6_4 ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 4)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_4 ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 4)" 'Ex4 P0 P1 P2 P3 P4 P5 = (ex6_4 ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 5) *)
 
@@ -192,7 +192,7 @@ inductive ex6_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→A3→
    | ex6_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → ex6_5 ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 5)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 5)" 'Ex5 P0 P1 P2 P3 P4 P5 = (ex6_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 6) *)
 
@@ -200,7 +200,7 @@ inductive ex6_6 (A0,A1,A2,A3,A4,A5:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2→A3
    | ex6_6_intro: ∀x0,x1,x2,x3,x4,x5. P0 x0 x1 x2 x3 x4 x5 → P1 x0 x1 x2 x3 x4 x5 → P2 x0 x1 x2 x3 x4 x5 → P3 x0 x1 x2 x3 x4 x5 → P4 x0 x1 x2 x3 x4 x5 → P5 x0 x1 x2 x3 x4 x5 → ex6_6 ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 6)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_6 ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 6)" 'Ex6 P0 P1 P2 P3 P4 P5 = (ex6_6 ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 7) *)
 
@@ -208,7 +208,7 @@ inductive ex6_7 (A0,A1,A2,A3,A4,A5,A6:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A2
    | ex6_7_intro: ∀x0,x1,x2,x3,x4,x5,x6. P0 x0 x1 x2 x3 x4 x5 x6 → P1 x0 x1 x2 x3 x4 x5 x6 → P2 x0 x1 x2 x3 x4 x5 x6 → P3 x0 x1 x2 x3 x4 x5 x6 → P4 x0 x1 x2 x3 x4 x5 x6 → P5 x0 x1 x2 x3 x4 x5 x6 → ex6_7 ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 7)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 7)" 'Ex7 P0 P1 P2 P3 P4 P5 = (ex6_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 8) *)
 
@@ -216,7 +216,7 @@ inductive ex6_8 (A0,A1,A2,A3,A4,A5,A6,A7:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1→A
    | ex6_8_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7. P0 x0 x1 x2 x3 x4 x5 x6 x7 → P1 x0 x1 x2 x3 x4 x5 x6 x7 → P2 x0 x1 x2 x3 x4 x5 x6 x7 → P3 x0 x1 x2 x3 x4 x5 x6 x7 → P4 x0 x1 x2 x3 x4 x5 x6 x7 → P5 x0 x1 x2 x3 x4 x5 x6 x7 → ex6_8 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 8)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_8 ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 8)" 'Ex8 P0 P1 P2 P3 P4 P5 = (ex6_8 ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (6, 9) *)
 
@@ -224,7 +224,7 @@ inductive ex6_9 (A0,A1,A2,A3,A4,A5,A6,A7,A8:Type[0]) (P0,P1,P2,P3,P4,P5:A0→A1
    | ex6_9_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 → ex6_9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (6, 9)" 'Ex P0 P1 P2 P3 P4 P5 = (ex6_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
+interpretation "multiple existental quantifier (6, 9)" 'Ex9 P0 P1 P2 P3 P4 P5 = (ex6_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5).
 
 (* multiple existental quantifier (7, 3) *)
 
@@ -232,7 +232,7 @@ inductive ex7_3 (A0,A1,A2:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→Prop) :
    | ex7_3_intro: ∀x0,x1,x2. P0 x0 x1 x2 → P1 x0 x1 x2 → P2 x0 x1 x2 → P3 x0 x1 x2 → P4 x0 x1 x2 → P5 x0 x1 x2 → P6 x0 x1 x2 → ex7_3 ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 3)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_3 ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 3)" 'Ex3 P0 P1 P2 P3 P4 P5 P6 = (ex7_3 ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 4) *)
 
@@ -240,7 +240,7 @@ inductive ex7_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3→
    | ex7_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → P5 x0 x1 x2 x3 → P6 x0 x1 x2 x3 → ex7_4 ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 4)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 4)" 'Ex4 P0 P1 P2 P3 P4 P5 P6 = (ex7_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 5) *)
 
@@ -248,7 +248,7 @@ inductive ex7_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2→A3
    | ex7_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → P6 x0 x1 x2 x3 x4 → ex7_5 ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 5)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 5)" 'Ex5 P0 P1 P2 P3 P4 P5 P6 = (ex7_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 6) *)
 
@@ -256,7 +256,7 @@ inductive ex7_6 (A0,A1,A2,A3,A4,A5:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A2
    | ex7_6_intro: ∀x0,x1,x2,x3,x4,x5. P0 x0 x1 x2 x3 x4 x5 → P1 x0 x1 x2 x3 x4 x5 → P2 x0 x1 x2 x3 x4 x5 → P3 x0 x1 x2 x3 x4 x5 → P4 x0 x1 x2 x3 x4 x5 → P5 x0 x1 x2 x3 x4 x5 → P6 x0 x1 x2 x3 x4 x5 → ex7_6 ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 6)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_6 ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 6)" 'Ex6 P0 P1 P2 P3 P4 P5 P6 = (ex7_6 ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 7) *)
 
@@ -264,7 +264,7 @@ inductive ex7_7 (A0,A1,A2,A3,A4,A5,A6:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→A1→A
    | ex7_7_intro: ∀x0,x1,x2,x3,x4,x5,x6. P0 x0 x1 x2 x3 x4 x5 x6 → P1 x0 x1 x2 x3 x4 x5 x6 → P2 x0 x1 x2 x3 x4 x5 x6 → P3 x0 x1 x2 x3 x4 x5 x6 → P4 x0 x1 x2 x3 x4 x5 x6 → P5 x0 x1 x2 x3 x4 x5 x6 → P6 x0 x1 x2 x3 x4 x5 x6 → ex7_7 ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 7)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 7)" 'Ex7 P0 P1 P2 P3 P4 P5 P6 = (ex7_7 ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 9) *)
 
@@ -272,7 +272,7 @@ inductive ex7_9 (A0,A1,A2,A3,A4,A5,A6,A7,A8:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A0→
    | ex7_9_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 → ex7_9 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 9)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 9)" 'Ex9 P0 P1 P2 P3 P4 P5 P6 = (ex7_9 ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (7, 10) *)
 
@@ -280,7 +280,7 @@ inductive ex7_10 (A0,A1,A2,A3,A4,A5,A6,A7,A8,A9:Type[0]) (P0,P1,P2,P3,P4,P5,P6:A
    | ex7_10_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8,x9. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → ex7_10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (7, 10)" 'Ex P0 P1 P2 P3 P4 P5 P6 = (ex7_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
+interpretation "multiple existental quantifier (7, 10)" 'Ex10 P0 P1 P2 P3 P4 P5 P6 = (ex7_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6).
 
 (* multiple existental quantifier (8, 4) *)
 
@@ -288,7 +288,7 @@ inductive ex8_4 (A0,A1,A2,A3:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2→A3
    | ex8_4_intro: ∀x0,x1,x2,x3. P0 x0 x1 x2 x3 → P1 x0 x1 x2 x3 → P2 x0 x1 x2 x3 → P3 x0 x1 x2 x3 → P4 x0 x1 x2 x3 → P5 x0 x1 x2 x3 → P6 x0 x1 x2 x3 → P7 x0 x1 x2 x3 → ex8_4 ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (8, 4)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
+interpretation "multiple existental quantifier (8, 4)" 'Ex4 P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_4 ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
 
 (* multiple existental quantifier (8, 5) *)
 
@@ -296,7 +296,7 @@ inductive ex8_5 (A0,A1,A2,A3,A4:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P7:A0→A1→A2
    | ex8_5_intro: ∀x0,x1,x2,x3,x4. P0 x0 x1 x2 x3 x4 → P1 x0 x1 x2 x3 x4 → P2 x0 x1 x2 x3 x4 → P3 x0 x1 x2 x3 x4 → P4 x0 x1 x2 x3 x4 → P5 x0 x1 x2 x3 x4 → P6 x0 x1 x2 x3 x4 → P7 x0 x1 x2 x3 x4 → ex8_5 ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (8, 5)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
+interpretation "multiple existental quantifier (8, 5)" 'Ex5 P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_5 ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
 
 (* multiple existental quantifier (8, 10) *)
 
@@ -304,7 +304,7 @@ inductive ex8_10 (A0,A1,A2,A3,A4,A5,A6,A7,A8,A9:Type[0]) (P0,P1,P2,P3,P4,P5,P6,P
    | ex8_10_intro: ∀x0,x1,x2,x3,x4,x5,x6,x7,x8,x9. P0 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P1 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P2 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P3 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P4 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P5 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P6 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → P7 x0 x1 x2 x3 x4 x5 x6 x7 x8 x9 → ex8_10 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?
 .
 
-interpretation "multiple existental quantifier (8, 10)" 'Ex P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
+interpretation "multiple existental quantifier (8, 10)" 'Ex10 P0 P1 P2 P3 P4 P5 P6 P7 = (ex8_10 ? ? ? ? ? ? ? ? ? ? P0 P1 P2 P3 P4 P5 P6 P7).
 
 (* multiple disjunction connective (3) *)