Let x0 of type ι be given.
Let x1 of type ι be given.
Apply unknownprop_f23dde3020cfe827bdc4db0338b279dd2c0f6c90742a195a1a7a614475669076 with
λ x2 . In (mul_nat x1 (ordsucc x2)) (mul_nat x0 (ordsucc x2)) leaving 2 subgoals.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x1,
0,
λ x2 x3 . In x3 (mul_nat x0 1) leaving 2 subgoals.
The subproof is completed by applying unknownprop_0e150139fedb8d7a0ae85e3054b4c73c936e7acb880ce730fb00a0093c9c6c27.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x0,
0,
λ x2 x3 . In (add_nat x1 (mul_nat x1 0)) x3 leaving 2 subgoals.
The subproof is completed by applying unknownprop_0e150139fedb8d7a0ae85e3054b4c73c936e7acb880ce730fb00a0093c9c6c27.
Apply unknownprop_4756ca8c34efd0461ee4f316febaf4ee77ac8f03a3f9f75c481b60c5f8500b17 with
x1,
λ x2 x3 . In (add_nat x1 x3) (add_nat x0 (mul_nat x0 0)).
Apply unknownprop_4756ca8c34efd0461ee4f316febaf4ee77ac8f03a3f9f75c481b60c5f8500b17 with
x0,
λ x2 x3 . In (add_nat x1 0) (add_nat x0 x3).
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x1,
λ x2 x3 . In x3 (add_nat x0 0).
Apply unknownprop_bad5adbbba30ab6e9c584ed350d824b3c3bff74e61c0a5380ac75f32855c37ee with
x0,
λ x2 x3 . In x1 x3.
The subproof is completed by applying H1.
Let x2 of type ι be given.
Apply unknownprop_077979b790f9097ea9250573e60509ec9410103c35a67e0558983ee18582fb09 with
x2.
The subproof is completed by applying H2.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x1,
ordsucc x2,
λ x3 x4 . In x4 (mul_nat x0 (ordsucc (ordsucc x2))) leaving 2 subgoals.
The subproof is completed by applying L4.
Apply unknownprop_3defe724d02ba276d9730f9f5a87e86e6bc0e48da350a99bdaaf13f339867dcf with
x0,
ordsucc x2,
λ x3 x4 . In (add_nat x1 (mul_nat x1 (ordsucc x2))) x4 leaving 2 subgoals.
The subproof is completed by applying L4.
Apply unknownprop_3069c6fa8dbd033f1c94555c93d580ac5c2fd979807cb20dbdb8dc4cc9b1517f with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply unknownprop_0b229518762ed7010020950c24a2d0fe47c44c7a7b255cdddc862baf12395763 with
x1,
ordsucc x2 leaving 2 subgoals.
The subproof is completed by applying L5.
The subproof is completed by applying L4.
Apply unknownprop_0b229518762ed7010020950c24a2d0fe47c44c7a7b255cdddc862baf12395763 with
x0,
ordsucc x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L4.
Apply unknownprop_3336121954edce0fefb5edee2ad1b426a9827aac09625122db0ff807b493dc73 with
x0,
mul_nat x0 (ordsucc x2) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L7.
Apply unknownprop_16d203cf35db7c43083950b8cdf3bc14c48faba5d53a8b40d54b8c3e00a23527 with
add_nat x0 (mul_nat x0 (ordsucc x2)),
add_nat x0 (mul_nat x1 (ordsucc x2)),
add_nat x1 (mul_nat x1 (ordsucc x2)) leaving 3 subgoals.
Apply unknownprop_4db127623a54dea607d4178c4cffe8099fa715d4dd5c11459d1bd4ea367db087 with
add_nat x0 (mul_nat x0 (ordsucc x2)).
The subproof is completed by applying L8.
Apply unknownprop_96cf1681687a72000e888b65b413651ac6a9efd1f56be6a7e59d74ac0cd27951 with
mul_nat x0 (ordsucc x2),
mul_nat x1 (ordsucc x2),
x0 leaving 3 subgoals.
The subproof is completed by applying L7.
The subproof is completed by applying H3.
The subproof is completed by applying H0.
Apply unknownprop_4091ebd6d94cd2a61820d5e9e5b329a35ceeb943e078c5c25a4c8d631106573d with
x0,
x1,
mul_nat x1 (ordsucc x2) leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying L6.