Abstract
In order to establish that ℒ[A] = ℒ[B] follows from a set of assumptions Γ often one provesA =B and then invokes the principle of substitution of equals for equals. It has been observed that in the ancillary proof ofA =B one is allowed to use, in addition to those assumptions of Γ which are free for ℒ, certain (open) sentencesP which may not be part of Γ and may not follow from Γ, but are related to the context ℒ. We show that in an appropriate formal system there is a closed form solution to the problem of determining precisely what sentencesP can be used. We say that those sentenceshold in the context ℒ under the set of assumptions Γ. We suggest how the solution could be exploited in an interactive theorem prover.
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Corella, F. What holds in a context?. J Autom Reasoning 10, 79–93 (1993). https://doi.org/10.1007/BF00881865
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DOI: https://doi.org/10.1007/BF00881865