Coq formalization of QRC1

This is a Coq formalization of the QRC1 quantified modal logic introduced in Quantified Reflection Calculus with one modality and further studied in An Escape from Vardanyan’s Theorem.

v0.1.0 includes:

• the syntax of quantified and strictly positive formulas;
• the notion of QRC1 proof;
• a proof that it is possible to conservatively add extra constants to the language;
• the notion of Kripke model for QRC1;
• a proof of Kripke soundness for QRC1;
• a proof of the Lindenbaum Lemma for QRC1; and
• a proof of the Pair Existence Lemma for QRC1.