let G, H be SimpleGraph; :: thesis: for n being Nat holds (MycielskianSeq G) . (n + 1) = Mycielskian ((MycielskianSeq G) . n)
let n be Nat; :: thesis: (MycielskianSeq G) . (n + 1) = Mycielskian ((MycielskianSeq G) . n)
set H = (MycielskianSeq G) . n;
consider myc being Function such that
A1: MycielskianSeq G = myc and
myc . 0 = G and
A2: for k being Nat
for G being SimpleGraph st G = myc . k holds
myc . (k + 1) = Mycielskian G by Def26;
thus (MycielskianSeq G) . (n + 1) = Mycielskian ((MycielskianSeq G) . n) by A1, A2; :: thesis: verum