induct: fixes P :: "'c mrexp3 \<Rightarrow> 'c mrexp3 \<Rightarrow> bool"   and a0 :: "'c mrexp3"   and a1 :: "'c mrexp3" assumes "P Zero3 Zero3"   and "P One3 One3"   and "\<And>m x m' y. P (Atom3 m x) (Atom3 m' y)"   and "\<And>r1 s1 uu_ uv_ r3 s3 uw_ ux_. \<lbrakk>P r1 r3; P s1 s3\<rbrakk> \<Longrightarrow> P (Plus3 r1 s1 uu_ uv_) (Plus3 r3 s3 uw_ ux_)"   and "\<And>r1 s1 uy_ uz_ r3 s3 va_ vb_. \<lbrakk>P r1 r3; P s1 s3\<rbrakk> \<Longrightarrow> P (Times3 r1 s1 uy_ uz_) (Times3 r3 s3 va_ vb_)"   and "\<And>r1 vc_ r3 vd_. P r1 r3 \<Longrightarrow> P (Star3 r1 vc_) (Star3 r3 vd_)"   and "P One3 Zero3"   and "\<And>v va. P One3 (Atom3 v va)"   and "\<And>v va vb vc. P One3 (Plus3 v va vb vc)"   and "\<And>v va vb vc. P One3 (Times3 v va vb vc)"   and "\<And>v va. P One3 (Star3 v va)"   and "\<And>v va. P (Atom3 v va) Zero3"   and "\<And>v va. P (Atom3 v va) One3"   and "\<And>v va vb vc vd ve. P (Atom3 v va) (Plus3 vb vc vd ve)"   and "\<And>v va vb vc vd ve. P (Atom3 v va) (Times3 vb vc vd ve)"   and "\<And>v va vb vc. P (Atom3 v va) (Star3 vb vc)"   and "\<And>v va vb vc. P (Plus3 v va vb vc) Zero3"   and "\<And>v va vb vc. P (Plus3 v va vb vc) One3"   and "\<And>v va vb vc vd ve. P (Plus3 v va vb vc) (Atom3 vd ve)"   and "\<And>v va vb vc vd ve vf vg. P (Plus3 v va vb vc) (Times3 vd ve vf vg)"   and "\<And>v va vb vc vd ve. P (Plus3 v va vb vc) (Star3 vd ve)"   and "\<And>v va vb vc. P (Times3 v va vb vc) Zero3"   and "\<And>v va vb vc. P (Times3 v va vb vc) One3"   and "\<And>v va vb vc vd ve. P (Times3 v va vb vc) (Atom3 vd ve)"   and "\<And>v va vb vc vd ve vf vg. P (Times3 v va vb vc) (Plus3 vd ve vf vg)"   and "\<And>v va vb vc vd ve. P (Times3 v va vb vc) (Star3 vd ve)"   and "\<And>v va. P (Star3 v va) Zero3"   and "\<And>v va. P (Star3 v va) One3"   and "\<And>v va vb vc. P (Star3 v va) (Atom3 vb vc)"   and "\<And>v va vb vc vd ve. P (Star3 v va) (Plus3 vb vc vd ve)"   and "\<And>v va vb vc vd ve. P (Star3 v va) (Times3 vb vc vd ve)"   and "P Zero3 One3"   and "\<And>v va. P (Atom3 v va) One3"   and "\<And>v va vb vc. P (Plus3 v va vb vc) One3"   and "\<And>v va vb vc. P (Times3 v va vb vc) One3"   and "\<And>v va. P (Star3 v va) One3"   and "\<And>v va. P Zero3 (Atom3 v va)"   and "\<And>v va. P One3 (Atom3 v va)"   and "\<And>vb vc vd ve v va. P (Plus3 vb vc vd ve) (Atom3 v va)"   and "\<And>vb vc vd ve v va. P (Times3 vb vc vd ve) (Atom3 v va)"   and "\<And>vb vc v va. P (Star3 vb vc) (Atom3 v va)"   and "\<And>v va vb vc. P Zero3 (Plus3 v va vb vc)"   and "\<And>v va vb vc. P One3 (Plus3 v va vb vc)"   and "\<And>vd ve v va vb vc. P (Atom3 vd ve) (Plus3 v va vb vc)"   and "\<And>vd ve vf vg v va vb vc. P (Times3 vd ve vf vg) (Plus3 v va vb vc)"   and "\<And>vd ve v va vb vc. P (Star3 vd ve) (Plus3 v va vb vc)"   and "\<And>v va vb vc. P Zero3 (Times3 v va vb vc)"   and "\<And>v va vb vc. P One3 (Times3 v va vb vc)"   and "\<And>vd ve v va vb vc. P (Atom3 vd ve) (Times3 v va vb vc)"   and "\<And>vd ve vf vg v va vb vc. P (Plus3 vd ve vf vg) (Times3 v va vb vc)"   and "\<And>vd ve v va vb vc. P (Star3 vd ve) (Times3 v va vb vc)"   and "\<And>v va. P Zero3 (Star3 v va)"   and "\<And>v va. P One3 (Star3 v va)"   and "\<And>vb vc v va. P (Atom3 vb vc) (Star3 v va)"   and "\<And>vb vc vd ve v va. P (Plus3 vb vc vd ve) (Star3 v va)"   and "\<And>vb vc vd ve v va. P (Times3 vb vc vd ve) (Star3 v va)" shows "P a0 a1"