Halliday & Matthiessen (2014: 546-7):
Like a proposition, a proposal may either be embedded as Qualifier to one of these nouns, as in the examples above, or may function on its own as a nominalisation e.g.You’ve said that one of your editorial rules is [[not to publish your buddies]].
Again, a first requirement is [[ to do no harm to organisational frameworks [[ that, through years of evolution, are finally at the stage [[ where they are supporting programs [[ that are actually helping us to get on with the business [[ of increasing understanding]] ]] ]] ]] ]].
The title for king fell out of use because its final requirement was [[ that the man [[ who aspires to be king]] would first pay all the debt [[ owed by every single man and every single woman in the community]] ]]
and we can construct similar pairs, for example(a) ||| he insisted || that they had to wait in line |||
(b) ||| he resented (the rule) [[that they had to wait in line ]]
where in (a) it is the ‘mental’ clause he insisted that does the projecting, while in (b) the projected clause is embedded. The ‘mental’ clause with the embedded fact clause is of the ‘emotive’ subtype, just as with propositions. But the ‘mental’ clause projecting the idea clause in (a) is not a ‘cognitive’ one but rather a ‘desiderative’ one. With ‘mental’ clauses, the general principle is that embedded fact clauses serve as Phenomenon in ‘emotive’ clauses, whether the facts are propositions or proposals; and that propositions are projected by ‘cognitive’ clauses whereas proposals are projected by ‘desiderative’ ones.
Note that insisted here serves as a verbal Process (projecting a locution clause), not a mental one (projecting an idea clause).