(*** eq_inv_pushs_sn *)
lemma gr_eq_inv_pushs_sn (n):
∀f1,g2. ⫯*[n] f1 ≡ g2 →
- â\88§â\88§ f1 â\89¡ ⫱*[n]g2 & ⫯*[n]⫱*[n]g2 = g2.
+ â\88§â\88§ f1 â\89¡ â«°*[n]g2 & ⫯*[n]â«°*[n]g2 = g2.
#n @(nat_ind_succ … n) -n /2 width=1 by conj/
#n #IH #f1 #g2 #H
elim (gr_eq_inv_push_sn … H) -H [|*: // ] #Hf10 *
(*** eq_inv_pushs_dx *)
lemma gr_eq_inv_pushs_dx (n):
∀f2,g1. g1 ≡ ⫯*[n] f2 →
- â\88§â\88§ ⫱*[n]g1 â\89¡ f2 & ⫯*[n]⫱*[n]g1 = g1.
+ â\88§â\88§ â«°*[n]g1 â\89¡ f2 & ⫯*[n]â«°*[n]g1 = g1.
#n @(nat_ind_succ … n) -n /2 width=1 by conj/
#n #IH #f2 #g1 #H
elim (gr_eq_inv_push_dx … H) -H [|*: // ] #Hf02 *