Subtraction in NatInt #119
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Why not |
Villetaneuse
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This only prevents to use the lemmas with an unqualified name, right? They would still appear in But maybe both is better. |
This is the revival of an old PR in former repository. We add two axioms in NatInt to restrict the models to exactly the integers and the natural numbers (with `pred 0 = 0`). This allows us to prove lemmas such as `sub_succ` and then prove many properties of `sub` which are shared between the natural numbers and the integers. The Natural and Integer parts of Numbers are modified in consequence. The result should be completely compatible except for `mul_sub_distr_l` which had different variable names in Integers and Natural (we chose to keep it as it was in Integers). We also remove references to old NZAxiomsSig modules. This needs more polishing, so still a draft: - the case of `mul_sub_distr_l` should be decided - removing some `Private_` lemmas is possible (e.g. with `Let`), this would result in a cleaner PR - check exactly the before/after for a user importing PeanoNat, etc
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This is the revival of an old PR in former repository.
We add two axioms in NatInt to restrict the models to exactly the integers and the natural numbers (with
pred 0 = 0). This allows us to prove lemmas such assub_succand then prove many properties ofsubwhich are shared between the natural numbers and the integers.The Natural and Integer parts of Numbers are modified in consequence. The result should be completely compatible except for
mul_sub_distr_lwhich had different variable names in Integers and Natural (we chose to keep it as it was in Integers).We also remove references to old NZAxiomsSig modules.
This needs more polishing, so still a draft:
mul_sub_distr_lshould be decidedPrivate_lemmas is possible (e.g. withLet), this would result in a cleaner PRFixes / closes #????