Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: From formal proofs to mathematical proofs: a safe, incremental way for
  building in first-order decision procedures   We investigate here a new version of the Calculus of Inductive Constructions
(CIC) on which the proof assistant Coq is based: the Calculus of Congruent
Inductive Constructions, which truly extends CIC by building in arbitrary
first-order decision procedures: deduction is still in charge of the CIC
kernel, while computation is outsourced to dedicated first-order decision
procedures that can be taken from the shelves provided they deliver a proof
certificate. The soundness of the whole system becomes an incremental property
following from the soundness of the certificate checkers and that of the
kernel. A detailed example shows that the resulting style of proofs becomes
closer to that of the working mathematician.

24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
17
The categories of this paper are: q-fin
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
36
The categories of this paper are: cmp-lg