Refactor Data.Vec.Properties : Add toList-injective and new lemmas

[jmougeot]

• Replace Data.List.Base as List and Data.List.Properties as List with shorter L aliases throughout the module for better readable proof

• Add new utility lemma toList-injective that proves vector equality from list equality using heterogeneous equality

• Add new equation-free lemmas that leverage toList-injective for cleaner proofs:

  • fromList-reverse: proves fromList (L.reverse xs) ≈[ L.length-reverse xs ] reverse (fromList xs)
  • ++-ʳ++-eqFree: proves associativity-like property for reverse-append without explicit equation parameter
  • ʳ++-ʳ++-eqFree: proves composition property for reverse-append operations

• Update all List. references to L. in function types and implementations

• Import Tactic.Cong module to support the cong! tactic used in several proofs

This change improves code readability and adds a fundamental lemma for reasoning about vector equality via list conversion, which is used in several proofs throughout the module.

[JacquesCarette]

Replace Data.List.Base as List and Data.List.Properties as List with shorter L aliases throughout the module for better readable proof

While I happen to like that, this goes specifically against the stdlib naming convention which states that it should be List.

import Tactic.Cong module to support the cong! tactic used in several proofs

It has been an (unwritten!) convention to not use tactics in fairly low-level parts of the library, as we don't want those parts of the library to depend on the Reflection machinery. The dependency graph is nasty enough as it is, we don't really want to make it worse.

[MatthewDaggitt]

Generally the lemmas look good, but I agree with @JacquesCarette point about the use of tactics.

[MatthewDaggitt]

Otherwise once the old lemma is added back, then it looks good to go!

[JacquesCarette]

Other than the missing CHANGELOG bit that @MatthewDaggitt asked for, and the cong!, this looks good to me too.