Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_01a114695ffc1947170447fdad5efc68e147fcc0454c56a0d7ea5b19e5fad219 with
x0,
x1,
u12,
u20,
and (x0 = u4) (x1 = u8) leaving 7 subgoals.
Apply nat_p_SNo with
x0.
The subproof is completed by applying H0.
Apply nat_p_SNo with
x1.
The subproof is completed by applying H1.
Apply nat_p_SNo with
u12.
The subproof is completed by applying nat_12.
Apply nat_p_SNo with
u20.
The subproof is completed by applying unknownprop_07ad204b3b4fc2b51cd8392b0e6a88916124d7f0f3dbf696bec5a683b0ea9dae.
The subproof is completed by applying H2.
The subproof is completed by applying H3.
Apply unknownprop_6502b005df6cab01356c9d955bc809f862844de5e4a01194bf49c9058d670f64 with
λ x2 x3 . x1 = x3 ⟶ x0 = add_SNo (mul_SNo u2 u12) (minus_SNo u20) ⟶ and (x0 = u4) (x1 = u8).
Apply unknownprop_1692dc98d264a82bacaf6d02c68843e5f1607f9095ce664ce240b86cf3e90e57 with
λ x2 x3 . x1 = u8 ⟶ x0 = add_SNo x3 (minus_SNo u20) ⟶ and (x0 = u4) (x1 = u8).
Apply unknownprop_caaed9cc542a41bb8c68b09f36dec250167b4be7de49834a0622f344dac85f46 with
λ x2 x3 . x1 = u8 ⟶ x0 = x3 ⟶ and (x0 = u4) (x1 = u8).
Apply andI with
x0 = u4,
x1 = u8 leaving 2 subgoals.
The subproof is completed by applying H5.
The subproof is completed by applying H4.