equal (invert_permut_body O) (λf. λm. if (m = (f O)) then O else O)

Axiom axiom_invert_permut_body_O : connectives.equal ((nat.nat -> nat.nat) -> nat.nat -> nat.nat) (invert_permut_body nat.O) (fun (f:(nat.nat -> nat.nat)) => fun (m:nat.nat) => bool.match_bool_type (nat.nat) nat.O nat.O (nat.eqb m (f nat.O)))

axiom axiom_invert_permut_body_O : (equal) ((nat -> nat) -> nat -> nat) ((invert_permut_body) (O) ) (\lambda f : nat -> nat. \lambda m : nat. (match_bool_type) (nat) (O) (O) ((eqb) m (f (O) )))

axiom axiom_invert_permut_body_O : (((connectives.equal) (((nat.nat) -> nat.nat) -> (nat.nat) -> nat.nat)) (((permutation.invert_permut_body) ) ((nat.O) ))) (fun (f : (nat.nat) -> nat.nat) , fun (m : nat.nat) , ((((bool.match_bool_type) (nat.nat)) ((nat.O) )) ((nat.O) )) ((((nat.eqb) ) (m)) ((f) ((nat.O) ))))

axiom_invert_permut_body_O : AXIOM connectives_sttfa_th.equal[[[nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat] -> [nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]]](permutation_sttfa.invert_permut_body(nat_sttfa_th.sttfa_O))((LAMBDA(f:[nat_sttfa_th.sttfa_nat -> nat_sttfa_th.sttfa_nat]):(LAMBDA(m:nat_sttfa_th.sttfa_nat):bool_sttfa_th.match_bool_type[nat_sttfa_th.sttfa_nat](nat_sttfa_th.sttfa_O)(nat_sttfa_th.sttfa_O)(nat_sttfa_th.eqb(m)(f(nat_sttfa_th.sttfa_O))))))

Printing for OpenTheory is not working at the moment.