theorem :: Introduction 'or' to premiss
  (X \/ {p} |-_IPC r & Y \/ {q} |-_IPC r) implies
    (X \/ Y) \/ {p 'or' q} |-_IPC r
proof
  set U = p 'or' q;
  set Z = X \/ Y;
  assume A1: (X \/ {p} |-_IPC r & Y \/ {q} |-_IPC r); then
A2: X |-_IPC p => r by Th53;
A4: X c= Z & Y c= Z by XBOOLE_1:7; then
A5: Z |-_IPC p => r by A2,Th66;
   Y |-_IPC q => r by A1,Th53; then
A6: Z |-_IPC q => r by A4,Th66;
   Z |-_IPC (p => r) => ((q => r) => (U => r)) by Th25; then
   Z |-_IPC (q => r) => (U => r) by A5,Th27; then
A9: Z |-_IPC U => r by A6,Th27;
   Z c= Z \/ {U} by XBOOLE_1:7; then
A11: Z \/ {U} |-_IPC U => r by A9,Th66;
  {U} |-_IPC U by Th65; then
  Z \/ {U} |-_IPC U by Th66,XBOOLE_1:7;
  hence thesis by A11,Th27;
end;
