Examples of bijection

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Because the single encoding judgement is functional in both directions, these functions are mutually inverse, yielding a bijection.
A permutation is a bijection from a finite set to itself.
There is a natural extension of this bijection to all positive formulas by induction, which we give in the following definition.
It is an injection but not necessary a bijection.
Terms are annotated with -abstraction is annotated that there exists a bijection which we leave unspecified.
To this end, we first need to extend the assignment function to be a bijection.
To invent the substitution domain, we may use any such bijection.
The bijection is based on rotation of circular words.
This restriction is a continuous bijection which respects geometry in the following sense.
The composition of two wobbling mappings has the same quality, and this also holds for the inverse of a wobbling bijection.
Moreover, if x is incommensurable, there is a natural bijection between the two orbits.
Two marked weighted dual trees are topologically equivalent when there exists a bijection between the two graphs which respect the intersection matrix and the indexations.
This correspondence is as close to a bijection as we could possibly hope for, in the following sense.
Once we know that is a bijection at the base sorts, it follows at the derived sorts too.
Conversely, we recover this natural bijection from any canonical translation when we consider terms equal up to renaming/simplification (in both calculi).
Note also our definition of isomorphisms is stronger than bijective p-maps: each component injection should become a symmetry-preserving/reflecting bijection.
It is easy to verify that each map is a bijection.
So we have a bijection between basic positive formulas, called positive negation.
We give a simple bijection to show that the equality can be extended to the distributions involved.

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