Let z be given.
Assume Hz.
We prove the intermediate claim Lp0z: F (proj0 z).
An
exact proof term for the current goal is
CD_proj0R z Hz.
We prove the intermediate claim Lp1z: F (proj1 z).
An
exact proof term for the current goal is
CD_proj1R z Hz.
We will
prove pa (proj0 z * proj0 1 + - conj (proj1 1) * proj1 z) (proj1 1 * proj0 z + proj1 z * conj (proj0 1)) = z.
rewrite the current goal using
CD_proj0_F F_0 1 F_1 (from left to right).
We will
prove pa (proj0 z * 1 + - conj (proj1 1) * proj1 z) (proj1 1 * proj0 z + proj1 z * conj 1) = z.
rewrite the current goal using
CD_proj1_F F_0 1 F_1 (from left to right).
We will
prove pa (proj0 z * 1 + - conj 0 * proj1 z) (0 * proj0 z + proj1 z * conj 1) = z.
rewrite the current goal using F_conj_0 (from left to right).
rewrite the current goal using F_conj_1 (from left to right).
We will
prove pa (proj0 z * 1 + - 0 * proj1 z) (0 * proj0 z + proj1 z * 1) = z.
rewrite the current goal using F_mul_1R (proj0 z) ?? (from left to right).
rewrite the current goal using F_mul_1R (proj1 z) ?? (from left to right).
rewrite the current goal using F_mul_0L (proj0 z) ?? (from left to right).
rewrite the current goal using F_mul_0L (proj1 z) ?? (from left to right).
We will
prove pa (proj0 z + - 0) (0 + proj1 z) = z.
rewrite the current goal using F_minus_0 (from left to right).
We will
prove pa (proj0 z + 0) (0 + proj1 z) = z.
rewrite the current goal using F_add_0L (proj1 z) ?? (from left to right).
rewrite the current goal using F_add_0R (proj0 z) ?? (from left to right).
We will prove pa (proj0 z) (proj1 z) = z.
Use symmetry.
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