from util import *


@apply
def apply(given, *, simplify=True):
    lhs, *limits = given.of(All[Expr > 0])
    shape = given.limits_shape
    rhs = ZeroMatrix(*shape, *lhs.shape)
    lhs = Lamda(lhs, *limits)    
    if simplify:
        lhs = lhs.simplify()
    return lhs > rhs


@prove
def prove(Eq):
    n = Symbol(integer=True, positive=True, given=True)
    i = Symbol(integer=True)
    f = Function(real=True)
    Eq << apply(All[i:n](f(i) > 0))

    Eq << ~Eq[1]

    Eq << ~Eq[-1]

    


if __name__ == '__main__':
    run()
# created on 2022-01-01
