[isabelle] substituting in hypotheses
Is there anything analogous to Isar's "subst" method that allows me to
perform a one-off substitution in a selected subgoal's hypothesis? Here
is a contrived example that could be proved trivially by auto, but
demonstrates what I'm trying to do in general:
lemma L1: "(x::nat)+1 = x+1+0"
lemma silly: "[| P(x+1::nat); R(%(x::nat). x+1) |] ==> R(%x. x+1+0)"
When proving "silly" I'd like to use lemma L1 to substitute "x+1+0" for
"x+1" in the second hypotheses. Note that
apply (simp only: L1)
will cause Isabelle to loop, and
apply (unfold L1)
fails. Even if unfold didn't fail here, it would likely also loop or
unfold the occurrence of x+1 in the other hypothesis and conclusion of
"silly", which I don't want.
Currently, the easiest way I know of to perform the substitution in the
hypothesis is through these cumbersome series of methods:
apply (erule_tac Q="R(%x. x+1)" in contrapos_pp)
apply (subst L1)
apply (erule_tac Q="R (%x. x+1+0)" in contrapos_nn)
Is there a more concise way to do this?
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