%% 6 points

proof implOr : (A | C) & (B => C)  =>  (A => B) => C
annotated proof implOr : (A | C) & (B => C)  =>  (A => B) => C
term implOr : (A | C) & (B => C)  =>  (A => B) => C

%% 8 points

proof curry : (A & B => C) => (A => B => C)
proof qcurry : ((?x:t. B(x)) => C) => (!x:t. B(x) => C)

term curry : (A & B => C) => (A => B => C)
term qcurry : ((?x:t. B(x)) => C) => (!x:t. B(x) => C)

%% 5 points

proof compose : (!x:t. A(x) => B(x))
             => (!x:t. B(x) => C(x))
             => !x:t. A(x) => C(x)

term compose : (!x:t. A(x) => B(x))
            => (!x:t. B(x) => C(x))
            => !x:t. A(x) => C(x)

%% 6 points

proof distribAllAnd : (!x:t. A(x) & B(x)) <=> (!x:t. A(x)) & (!x:t. B(x))
proof distribExAnd1 : (?x:t. A(x) & B(x)) => (?x:t. A(x)) & (?x:t. B(x))