Inversion lemmas for bind and iter in ictree

Develop and prove sound inversion lemmas for the monadic bind operator and the iter combinator in the ictree model to support forward reasoning within Ticl.

Background

The paper presents a broad set of backward-reasoning structural lemmas for ictree combinators and Ticl operators, and some bidirectional lemmas for constructors. These lemmas facilitate modular verification but primarily support backward reasoning.

To improve forward reasoning capabilities, the authors explicitly conjecture the existence of useful inversion lemmas for the bind operator and the iter combinator, leaving their development for future work. Such lemmas would enable deriving properties of program components from known properties of composed terms.