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Cancelable elements are a new way of proving local updates, by
removing some cancellable element of the global state, provided that
we own it and we are willing to lose this ownership.

Identity-free elements are an auxiliary that is necessary to prove that
[Some x] is cancelable.

For technical reasons, these two notions are not defined exactly like
what one might expect, but also take into account validity. Otherwise,
an exclusive element would not be cancelable or idfree, which is
rather confusing.

This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

Use COFEs only for the recursive domain equation solver

This allows us to factor out properties about connectives that
commute with the big operators.

This is more consistent with the definition of the extension order, which
is also defined in terms of an existential.

be the same as ↔.

This is a fairly intrusive change, but at least makes notations more
consistent, and often shorter because fewer parentheses are needed. Note
that viewshifts already had the same precedence as →.