Research proof index

Given an infinite sequence of non-empty finite executions of algorithm a, if all messages with destinations in ps that are in-flight at the beginning of each finite execution are delivered in that finite execution, then those finite executions can be concatenated into an infinite execution of a in which every process in ps is fair.

Whenever the message carrying the input value for process 0 is enabled in a state, a message carrying that value is eventually sent to every process p by process 0.

Whenever a message carrying a value sent by process 0 is enabled at a process p, p eventually decides on that value.

If the edges of an infinite complete graph is assigned a finite number of colors, then there must exist a color c and an infinite set s of vertices such that the edge between any two vertices of s is assigned the same color c.

Subtyping of substitutions.

Invert the typing of an abstraction.