Let x0 of type ι be given.
Apply add_nat_1_1_2 with
λ x1 x2 . mul_nat x1 x0 = add_nat x0 x0.
Apply mul_add_nat_distrR with
1,
1,
x0,
λ x1 x2 . x2 = add_nat x0 x0 leaving 4 subgoals.
The subproof is completed by applying nat_1.
The subproof is completed by applying nat_1.
The subproof is completed by applying H0.
Apply unknownprop_6e31f7e63da1d74f4ea3ef967162bc5821029ffe1e451b13664a6e51a570dea7 with
x0,
λ x1 x2 . add_nat x2 x2 = add_nat x0 x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H1.