let A be QC-alphabet ; :: thesis: for F being Element of QC-WFF A
for G1, G2 being Subformula of F holds { (t ^ s) where t is Entry_Point_in_Subformula_Tree of G1, s is Element of dom (tree_of_subformulae G1) : s in G1 -entry_points_in_subformula_tree_of G2 } c= entry_points_in_subformula_tree G2
let F be Element of QC-WFF A; :: thesis: for G1, G2 being Subformula of F holds { (t ^ s) where t is Entry_Point_in_Subformula_Tree of G1, s is Element of dom (tree_of_subformulae G1) : s in G1 -entry_points_in_subformula_tree_of G2 } c= entry_points_in_subformula_tree G2
let G1, G2 be Subformula of F; :: thesis: { (t ^ s) where t is Entry_Point_in_Subformula_Tree of G1, s is Element of dom (tree_of_subformulae G1) : s in G1 -entry_points_in_subformula_tree_of G2 } c= entry_points_in_subformula_tree G2
{ (t ^ s) where t is Entry_Point_in_Subformula_Tree of G1, s is Element of dom (tree_of_subformulae G1) : s in G1 -entry_points_in_subformula_tree_of G2 } = { (t ^ s) where t is Element of dom (tree_of_subformulae F), s is Element of dom (tree_of_subformulae G1) : ( t in F -entry_points_in_subformula_tree_of G1 & s in G1 -entry_points_in_subformula_tree_of G2 ) } by Th39;
hence { (t ^ s) where t is Entry_Point_in_Subformula_Tree of G1, s is Element of dom (tree_of_subformulae G1) : s in G1 -entry_points_in_subformula_tree_of G2 } c= entry_points_in_subformula_tree G2 by Th29; :: thesis: verum