A simplification tactic for Z-module equations, specific to Z #17
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pi8027
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Jun 30, 2023
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| (forall zero add vm', zero = zeroG -> add = addG -> vm' = vm -> | ||
| let norm := ZMnorm (AGAdd e1 (AGOpp e2)) in | ||
| let '(xs, ys) := ZMsimpl_aux vm' norm in | ||
| sum zero add xs = sum zero add ys) -> |
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This is the proof obligation of the Z_zmodule_simplify tactic: zero, add, and vm' are abstracted out to make sure that they will not be reduced. I thought that norm should be reduced by vm_compute, and the other part should be reduced by lazy or compute because its readback seems to be costly.
It is quite intricate, so should be documented in detail.
pi8027
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Jun 30, 2023
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| intros zero add vm zeroE addE vmE norm; | ||
| vm_compute in norm; compute; | ||
| rewrite zeroE, addE, vmE; clear zero add vm zeroE addE vmE norm. |
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And this is the normalization of the proof obligation.
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This PR implements the
Z_zmodule_simplifytactic. For example, it turns a goal of the forminto
This kind of reflexive tactic leaving a proof obligation needs to simplify the obligation carefully. I'm not sure whether the current implementation is the best way to do so.