@nm To illustrate the action:

subsop(1=a,[2,1]=b,[2,2]=c,[2,3]=d,expr);
subsop(1=3, 2=b,3=c,4=d, expr);

@nm If you do not recognize the object you are manipulating recognizing the result would be a mystery. Maple uses automatic simplification, meaning all numeric constants are multiplied automatically. The constant of multiplication is operand 1. Your operation removes it and introduces an additional new multiplier. Your operation can not be completed as a substitution.

@Preben Alsholm If what you are saying is true then the purpose of assume mechanism is completely defeated.

You need to repost as text or file.

I suspect integral of 
(-(2/3)*t^2-(2/9)*t-4/27)*exp(-(3/2)*t)+4/27+(1/27)*(4*2^(-(1/2)*alpha)*3^((1/2)*alpha)*t^(-(1/2)*alpha)*(-2+alpha)*WhittakerM(-(1/2)*alpha, -(1/2)*alpha+1/2, (3/2)*t)-6*exp(-(3/4)*t)*((-2+alpha)*t^(1-alpha)+3*t^(2-alpha)))*exp(-(3/4)*t)/GAMMA(3-alpha);
has no closed form.

@Jesús Guillera How do you define minimal?

Can you post screenshots? Please do not post arbitrary file types on the forum.

I receive a result of FAIL in Maple 2017 for the following:

is(m > 0) assuming n>1, m>n*(n-1)/2;

@vv Assume facility DOES NOT do intermediate steps. To demonstrate:

restart;
# _EnvTry := true;  # useless
assume(a>0, b>0, a*b<1,c=a*b);
is(c>0),is(c<1);
is( (1 + sqrt(1-a^3*b^3))/(a*b) >0 ); # FAIL   ?
is( (1 + sqrt(1-a*b))/(a*b) >0 );     # FAIL   ?
is( (1 + sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a*b)) >0 );           # true
is( (1 + sqrt(1-a*b)) >0 );           # true

restart;
# _EnvTry := true;  # useless
assume(a>0, b>0, a*b<1, c=a*b, c>0, c<1);
is(c>0), is(c<1);
is( (1 + sqrt(1-a^3*b^3))/(a*b) >0 ); # FAIL   ?
is( (1 + sqrt(1-a*b))/(a*b) >0 );     # FAIL   ?
is( (1 + sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a^2*b^2)) >0 );       # false ??
is( (1 - sqrt(1-a*b)) >0 );           # true
is( (1 + sqrt(1-a*b)) >0 );           # true

The builtin command in Maple is the Maple language.

applyrule([[]=Q, [Q]=Q],x);
eval['recurse'](x,[[]=Q, [Q]=Q]);
 

@sursumCorda Are you saying the rules can contain f=d and f=g simultaneously?

Note: allvalues(polyroots) will generate 72 different permutations of the roots. 72 matches the Galois group order.