Merge PR #10445: Split constructive and classical axioms for real numbers

Ack-by: Zimmi48
Ack-by: silene

1 files changed, 12 insertions, 0 deletions

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+- New module `Reals.ConstructiveCauchyReals` defines constructive real numbers
+  by Cauchy sequences of rational numbers. Classical real numbers are now defined
+  as a quotient of these constructive real numbers, which significantly reduces
+  the number of axioms needed (see `Reals.Rdefinitions` and `Reals.Raxioms`),
+  while preserving backward compatibility.
+
+  Futhermore, the new axioms for classical real numbers include the limited
+  principle of omniscience (`sig_forall_dec`), which is a logical principle
+  instead of an ad hoc property of the real numbers.
+
+  See `#10445 <https://github.com/coq/coq/pull/10445>`_, by Vincent Semeria,
+  with the help and review of Guillaume Melquiond and Bas Spitters.