Theory VectorSpace.FunctionLemmas

section ‹Basic lemmas about functions›

theory FunctionLemmas

imports Main

text ‹These are used in simplification. Note that the difference from Pi-mem is that the statement
about the function comes first, so Isabelle can more easily figure out what $S$ is.›

lemma PiE_mem2: "f  SE T  x  S  f x  T"
  unfolding PiE_def by auto
lemma Pi_mem2: "f  S T  x  S  f x  T"
  unfolding Pi_def by auto