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Extra assumptions are simply discarded for now.
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Parameters must follow the relation symbol and be surrounded by braces, like so: `\rel{x}{y}{z}`.
This attempt is still brittle/broken in a few ways:
- It makes using braces in creative ways in mixfix notation ambiguous.
- It does not verify that the parameters are used in a consistent manner for each symbol. It essentially allows users to define `a\MyRel b` and `a\MyRel{x} b` (and ones with even more parameters).
- It allows parameters for all relation symbols, even for those where it makes no sense in ordinary TeX markup, e.g. `a <{x} b`.
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Use an `\iff`-calc to speed up `union_as_unions`. Also remove `in_implies_neq` which seems to interact badly with the choice axiom used by superposition-based proofs like Vampire in cut-down problems.
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Since Latex has a really specify syntax for
\begin{cases} ... \end{cases}
The math mode in tokenizing had to be setup correctly.
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Finalised the proof output and goals.
The Local Function definition now producces a Function f with the right
domain and range, together with the rules presented in cases.
Then proof goal of this local definition is set to
for all x we have x is element of dom(f) if and only if x is in exactly one of the subdomains.
This suffices as welldefindness check on f, besides the right range.
Further checks that should be implemented are the correct range of the function.
And optional subproof such that the presented goal can be check easily.
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since now some could define a function with overlapping
and worng subdomains
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But the Proof that the domain of the local function
is not right. Also if in the definition of our local
function we just use f(x) = x then we get a technical
ambigus parse
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function defintion from abstract to internal
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for local functions and a abstract type in abstract.hs
for the proof data structure.
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