Section resultats_iso_image.
Variable X V R : Ensf.
Variable S : Elt.
Variable f : Elt -> Elt.
Let Gim := imageGram f X V R S.
Let Xim := fst Gim.
Let Gim2 := snd Gim.
Let Vim := fst Gim2.
Let Gim3 := snd Gim2.
Let Rim := fst Gim3.
Let Sim := snd Gim3.
Let invf := inv (union X V) (union Xim Vim) f.
Let Gim' := imageGram invf Xim Vim Rim Sim.
Let Xim' := fst Gim'.
Let Gim2' := snd Gim'.
Let Vim' := fst Gim2'.
Let Gim3' := snd Gim2'.
Let Rim' := fst Gim3'.
Let Sim' := snd Gim3'.
Hypothesis Gram : isGram X V R S.
Proof isGram4 X V R S Gram.
Hypothesis Mono : is_mono (union X V) f.

Lemma inter_Xim_Vim_empty : inter Xim Vim empty.