| 1 | vars S, T : Type |
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| 2 | types Bool; |
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| 3 | Pred S := S ->? Unit; |
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| 4 | Set S := S ->? Unit |
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| 5 | ops True, False : Bool |
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| 6 | ops emptySet : Set S; |
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| 7 | {__} : S -> Set S; |
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| 8 | __isIn__ : S * Set S ->? Unit; |
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| 9 | __subset__ : Pred (Set (S) * Set (S)); |
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| 10 | __union__, __intersection__, __\\__ : Set S * Set S -> Set S; |
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| 11 | __disjoint__ : Pred (Set (S) * Set (S)); |
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| 12 | __*__ : Set S * Set T -> Set (S * T); |
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| 13 | __disjointUnion__ : Set S * Set S -> Set (S * Bool); |
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| 14 | inl, inr : S -> S * Bool |
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| 15 | forall x, x' : S; y : T; s, s' : Set S; t : Set T |
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| 16 | . not x isIn emptySet |
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| 17 | . x isIn { x' } <=> x = x' |
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| 18 | . x isIn s <=> s x |
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| 19 | . s subset s' <=> forall x : S . x isIn s => x isIn s' |
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| 20 | . x isIn (s union s') <=> x isIn s \/ x isIn s' |
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| 21 | . x isIn (s intersection s') <=> x isIn s /\ x isIn s' |
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| 22 | . x isIn (s \\ s') <=> x isIn s /\ not x isIn s' |
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| 23 | . s disjoint s' <=> s intersection s' = emptySet |
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| 24 | . (x, y) isIn (s * t) <=> x isIn s /\ y isIn t |
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| 25 | . inl x = (x, False) |
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| 26 | . inr x = (x, True); |
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| 27 | types |
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| 28 | Bool : Type; |
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| 29 | Set : Type -> Type |
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| 30 | type |
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| 31 | Set := \ S : Type . S ->? Unit |
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| 32 | vars |
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| 33 | S : Type %(var_1)%; |
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| 34 | T : Type %(var_2)% |
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| 35 | op False : Bool %(op)% |
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| 36 | op True : Bool %(op)% |
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| 37 | op __*__ : forall S : Type; T : Type . Set S * Set T -> Set (S * T) |
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| 38 | %(op)% |
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| 39 | op __\\__ : forall S : Type . Set S * Set S -> Set S %(op)% |
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| 40 | op __disjoint__ : forall S : Type . Pred (Set S * Set S) %(op)% |
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| 41 | op __disjointUnion__ : forall S : Type |
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| 42 | . Set S * Set S -> Set (S * Bool) |
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| 43 | %(op)% |
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| 44 | op __intersection__ : forall S : Type . Set S * Set S -> Set S |
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| 45 | %(op)% |
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| 46 | op __isIn__ : forall S : Type . S * Set S ->? Unit %(op)% |
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| 47 | op __subset__ : forall S : Type . Pred (Set S * Set S) %(op)% |
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| 48 | op __union__ : forall S : Type . Set S * Set S -> Set S %(op)% |
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| 49 | op emptySet : forall S : Type . Set S %(op)% |
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| 50 | op inl : forall S : Type . S -> S * Bool %(op)% |
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| 51 | op inr : forall S : Type . S -> S * Bool %(op)% |
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| 52 | op {__} : forall S : Type . S -> Set S %(op)% |
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| 53 | forall S : Type; x : S . not x isIn emptySet |
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| 54 | forall S : Type; x : S; x' : S . x isIn { x' } <=> x = x' |
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| 55 | forall S : Type; s : Set S; x : S . x isIn s <=> s x |
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| 56 | forall S : Type; s : Set S; s' : Set S |
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| 57 | . s subset s' <=> forall x : S . x isIn s => x isIn s' |
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| 58 | forall S : Type; s : Set S; s' : Set S; x : S |
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| 59 | . x isIn (s union s') <=> x isIn s \/ x isIn s' |
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| 60 | forall S : Type; s : Set S; s' : Set S; x : S |
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| 61 | . x isIn (s intersection s') <=> x isIn s /\ x isIn s' |
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| 62 | forall S : Type; s : Set S; s' : Set S; x : S |
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| 63 | . x isIn (s \\ s') <=> x isIn s /\ not x isIn s' |
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| 64 | forall S : Type; s : Set S; s' : Set S |
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| 65 | . s disjoint s' <=> s intersection s' = emptySet |
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| 66 | forall S : Type; T : Type; s : Set S; t : Set T; x : S; y : T |
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| 67 | . (x, y) isIn (s * t) <=> x isIn s /\ y isIn t |
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| 68 | forall S : Type; x : S . inl x = (x, False) |
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| 69 | forall S : Type; x : S . inr x = (x, True) |
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| 70 | ### Hint 1.6, is type variable 'S' |
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| 71 | ### Hint 1.8, is type variable 'T' |
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| 72 | ### Hint 3.14, rebound type variable 'S' |
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| 73 | ### Hint 3.8, redeclared type 'Pred' |
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| 74 | ### Hint 4.13, rebound type variable 'S' |
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| 75 | ### Hint 9.18, |
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| 76 | no kind found for 'S' |
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| 77 | expected: {Cpo} |
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| 78 | found: {Type} |
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| 79 | ### Hint 9.18, |
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| 80 | no kind found for 'S' |
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| 81 | expected: {Cppo} |
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| 82 | found: {Type} |
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| 83 | ### Hint 10.25-10.29, |
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| 84 | no kind found for 'Set S' |
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| 85 | expected: {Cpo} |
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| 86 | found: {Type} |
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| 87 | ### Hint 10.25-10.29, |
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| 88 | no kind found for 'Set S' |
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| 89 | expected: {Cppo} |
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| 90 | found: {Type} |
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| 91 | ### Hint 11.46-11.50, |
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| 92 | no kind found for 'Set S' |
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| 93 | expected: {Cpo} |
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| 94 | found: {Type} |
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| 95 | ### Hint 11.46-11.50, |
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| 96 | no kind found for 'Set S' |
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| 97 | expected: {Cppo} |
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| 98 | found: {Type} |
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| 99 | ### Hint 11.46-11.50, |
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| 100 | no kind found for 'Set S' |
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| 101 | expected: {Cpo} |
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| 102 | found: {Type} |
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| 103 | ### Hint 11.46-11.50, |
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| 104 | no kind found for 'Set S' |
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| 105 | expected: {Cppo} |
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| 106 | found: {Type} |
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| 107 | ### Hint 11.46-11.50, |
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| 108 | no kind found for 'Set S' |
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| 109 | expected: {Cpo} |
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| 110 | found: {Type} |
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| 111 | ### Hint 11.46-11.50, |
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| 112 | no kind found for 'Set S' |
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| 113 | expected: {Cppo} |
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| 114 | found: {Type} |
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| 115 | ### Hint 12.28-12.32, |
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| 116 | no kind found for 'Set S' |
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| 117 | expected: {Cpo} |
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| 118 | found: {Type} |
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| 119 | ### Hint 12.28-12.32, |
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| 120 | no kind found for 'Set S' |
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| 121 | expected: {Cppo} |
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| 122 | found: {Type} |
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| 123 | ### Hint 13.15-13.19, |
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| 124 | no kind found for 'Set S' |
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| 125 | expected: {Cpo} |
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| 126 | found: {Type} |
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| 127 | ### Hint 13.15-13.19, |
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| 128 | no kind found for 'Set S' |
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| 129 | expected: {Cppo} |
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| 130 | found: {Type} |
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| 131 | ### Hint 13.37, |
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| 132 | no kind found for 'S' |
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| 133 | expected: {Cpo} |
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| 134 | found: {Type} |
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| 135 | ### Hint 13.37, |
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| 136 | no kind found for 'S' |
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| 137 | expected: {Cppo} |
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| 138 | found: {Type} |
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| 139 | ### Hint 14.28-14.32, |
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| 140 | no kind found for 'Set S' |
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| 141 | expected: {Cpo} |
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| 142 | found: {Type} |
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| 143 | ### Hint 14.28-14.32, |
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| 144 | no kind found for 'Set S' |
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| 145 | expected: {Cppo} |
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| 146 | found: {Type} |
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| 147 | ### Hint 14.50, |
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| 148 | no kind found for 'S' |
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| 149 | expected: {Cpo} |
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| 150 | found: {Type} |
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| 151 | ### Hint 14.50, |
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| 152 | no kind found for 'S' |
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| 153 | expected: {Cppo} |
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| 154 | found: {Type} |
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| 155 | ### Hint 15.22, |
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| 156 | no kind found for 'S' |
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| 157 | expected: {Cpo} |
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| 158 | found: {Type} |
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| 159 | ### Hint 15.22, |
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| 160 | no kind found for 'S' |
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| 161 | expected: {Cppo} |
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| 162 | found: {Type} |
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| 163 | ### Hint 15.22, |
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| 164 | no kind found for 'S' |
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| 165 | expected: {Cpo} |
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| 166 | found: {Type} |
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| 167 | ### Hint 15.22, |
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| 168 | no kind found for 'S' |
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| 169 | expected: {Cppo} |
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| 170 | found: {Type} |
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| 171 | ### Hint 16.11, not a class 'S' |
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| 172 | ### Hint 16.14, not a class 'S' |
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| 173 | ### Hint 16.19, not a class 'T' |
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| 174 | ### Hint 16.24, not a kind 'Set (S)' |
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| 175 | ### Hint 16.27, not a kind 'Set (S)' |
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| 176 | ### Hint 16.37, not a kind 'Set (T)' |
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| 177 | ### Hint 20.32, not a class 'S' |
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| 178 | ### Hint 20.31, rebound variable 'x' |
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