set,higher-order-functions,isabelle,theorem-proving,isar

HOL types cannot depend on values. So if you want to define a quotient type for an arbitrary non-empty set S and equivalence relation equiv using quotient_type, the arbitrary part must stay at the meta-level. Thus, S and equiv can either be axiomatized or defined such that you can convince...

proof,agda,idris,proof-of-correctness,isar

Coq has extensive libraries covering real analysis. Various developments come to mind: the standard library and projects building on it such as the now defunct coqtail project [1] (with extensive coverage of power series and quite a bit of work on Complex numbers) or the more recent coquelicot. All of...

The error is not weird at all. Just have a look at the term that is represented by ?thesis (via term "?thesis") "λd k l. 0 < d ⟶ ¬ 2 * k + 1 ≤ 2 * l ⟶ 2 * l ≠ 1 ⟶ - (2 * l)...

proof,isabelle,theorem-proving,isar

It mostly depends on whether you are using the archaic (sorry for that ;)) apply-style or proper structured Isar for proving. I will give a small example to cover both styles. Assume you wanted to prove lemma "A & B" Where A and B just serve as placeholders for potentially...

Answer B: Building on HOL, with an Improvised J Syntax Clarification is good, but I don't like to do the handshaking necessary to do it. My first answer below was largely based on your phrase, "a completely new syntax", and I think it's half of an answer to a question...