Definition id3 := 1 : {perm cube}.Definition s05 := (perm S05_inj).Definition s14 : {perm cube}.Definition s23 := (perm (inv_inj S23_inv)).Definition r05 := (perm R05_inj).Definition r14 := (perm R14_inj).Definition r23 := (perm R23_inj).Definition r50 := (perm R50_inj).Definition r41 := (perm R41_inj).Definition r32 := (perm R32_inj).Definition r024 := (perm R024_inj).Definition r042 := (perm R042_inj).Definition r012 := (perm R012_inj).Definition r021 := (perm R021_inj).Definition r031 := (perm R031_inj).Definition r013 := (perm R013_inj).Definition r043 := (perm R043_inj).Definition r034 := (perm R034_inj).Definition s1 := (perm (inv_inj S1_inv)).Definition s2 := (perm (inv_inj S2_inv)).Definition s3 := (perm (inv_inj S3_inv)).Definition s4 := (perm (inv_inj S4_inv)).Definition s5 := (perm (inv_inj S5_inv)).Definition s6 := (perm (inv_inj S6_inv)).

Lemma S0_inv : involutive S0f.