In the paper "Parameter Elimination in Higher Order Existential Paths" https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/parameter-elimination-in-higher-order-existential-paths.pdf, the notation differs from the one used in "Universal Existential Paths" https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/universal-existential-paths.pdf The distinction should be clarified to avoid ambiguous use of terminology.
In the paper "Parameter Elimination in Higher Order Existential Paths" https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/parameter-elimination-in-higher-order-existential-paths.pdf, the notation differs from the one used in "Universal Existential Paths" https://github.com/advancedresearch/path_semantics/blob/master/papers-wip/universal-existential-paths.pdf
The distinction should be clarified to avoid ambiguous use of terminology.