## .1 Natural Deduction

by
We Characterize Equality

### BibTeX

@MISC{Equality_.1natural,

author = {We Characterize Equality},

title = {.1 Natural Deduction},

year = {}

}

### OpenURL

### Abstract

108 Equality Symmetrically, we can also replaces of occurrences of t by s. ` s : = t ` [t=x]A : = E 2 ` [s=x]A It might seem that this second rule is redundant, and in some sense it is. In particular, it is a derivable rule of the calculus with only : = E 1 : ` s : = t : = I ` s : = s : = E 1 ` t : = s ` [t=x]A : = E 1 ` [s=x]A However, this deduction is not normal (as defined below), and without the second elimination rule the normalization theorem would not hold and cut elimination in the sequent calculus would f