Let x0 of type ι be given.
Apply unknownprop_adc51df32e37a02ae01a7627d71f293cbf548824fcf0d70ccbf318430642e27c with
x0,
1,
λ x1 x2 . x2 = mul_nat x0 x0 leaving 2 subgoals.
The subproof is completed by applying unknownprop_8d353ccfb170ea018406af7266d499508cf5be2cebcac5c8a89ccd16a50d0251.
Apply unknownprop_859435fbf9780d9b77e6cf1223ba58a1a23713d4aea33f4f1e1a4aeb86a3c2ee with
x0,
λ x1 x2 . mul_nat x0 x2 = mul_nat x0 x0.
Let x1 of type ι → ι → ο be given.
The subproof is completed by applying H0.