let f, g, h be Function; :: thesis: for A being set
for F being Function st f | A = g | A holds
(F .: (f,h)) | A = (F .: (g,h)) | A
let A be set ; :: thesis: for F being Function st f | A = g | A holds
(F .: (f,h)) | A = (F .: (g,h)) | A
let F be Function; :: thesis: ( f | A = g | A implies (F .: (f,h)) | A = (F .: (g,h)) | A )
assume A1: f | A = g | A ; :: thesis: (F .: (f,h)) | A = (F .: (g,h)) | A
thus (F .: (f,h)) | A = F * (<:f,h:> | A) by RELAT_1:112
.= F * <:(f | A),h:> by Th10
.= F * (<:g,h:> | A) by A1, Th10
.= (F .: (g,h)) | A by RELAT_1:112 ; :: thesis: verum