[isabelle] Conditional simplification of constants
I have a constant f :: (real â real) â (real â real) set.
I also have the following lemma for the behaviour of f on constant
lemma f_const: "c â 0 â f (Î_. c) = f(Î_. 1)"
I want to automatically normalise every term of the form "f (Î_. c)" to
"f (Î_. 1)" with the simplifier.
However, adding f_const to the simplifier does not work, because then
the simplifier will loop rewriting "f (Î_. 1)" to itself.
I therefore tried the following rule:
lemma f_const': "c â 0 â c â 1 â f (Î_. c) = f(Î_. 1)"
That seems to work better in the simpset, but the simplifier still
occasionally loops. Swapping "c â 0" and "c â 1" in the premises does
not seem to change that.
Is there a way to get the simplifier to only rewrite if "c" is not equal
to 1? (equal on the expression level, not the term level. Rewriting "f
(Î_. 0+1)" to "f (Î_. 1)" is fine, but rewriting "f (Î_. 1)" to "f (Î_.
1)" is not) Should I write a simproc to do this? Or is there a better way?
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