include('Axioms/SET010^0.ax').
thf(v1_xreal_0_type, type, v1_xreal_0: $i > $o).
thf(k17_sin_cos_type, type, k17_sin_cos: $i > $i).
thf(k6_xcmplx_0_type, type, k6_xcmplx_0: $i > $i > $i).
thf(k3_xcmplx_0_type, type, k3_xcmplx_0: $i > $i > $i).
thf(k20_sin_cos_type, type, k20_sin_cos: $i > $i).
thf(k2_xcmplx_0_type, type, k2_xcmplx_0: $i > $i > $i).
thf(t83_sin_cos, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( (= @  (k20_sin_cos @  ( (k6_xcmplx_0 @ A)  @ B) ) )  @  ( (k2_xcmplx_0 @  ( (k3_xcmplx_0 @  (k20_sin_cos @ A) )  @  (k20_sin_cos @ B) ) )  @  ( (k3_xcmplx_0 @  (k17_sin_cos @ A) )  @  (k17_sin_cos @ B) ) ) ) ) ) ) ) , file(sin_cos, t83_sin_cos)).
thf(t82_sin_cos, axiom,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( (= @  (k17_sin_cos @  ( (k6_xcmplx_0 @ A)  @ B) ) )  @  ( (k6_xcmplx_0 @  ( (k3_xcmplx_0 @  (k17_sin_cos @ A) )  @  (k20_sin_cos @ B) ) )  @  ( (k3_xcmplx_0 @  (k20_sin_cos @ A) )  @  (k17_sin_cos @ B) ) ) ) ) ) ) ) , file(sin_cos, t82_sin_cos)).
thf(t3_complex2, conjecture,   (! [A: $i] :  ( (v1_xreal_0 @ A)  =>  (! [B: $i] :  ( (v1_xreal_0 @ B)  =>  ( ( (= @  (k17_sin_cos @  ( (k6_xcmplx_0 @ A)  @ B) ) )  @  ( (k6_xcmplx_0 @  ( (k3_xcmplx_0 @  (k17_sin_cos @ A) )  @  (k20_sin_cos @ B) ) )  @  ( (k3_xcmplx_0 @  (k20_sin_cos @ A) )  @  (k17_sin_cos @ B) ) ) )  &  ( (= @  (k20_sin_cos @  ( (k6_xcmplx_0 @ A)  @ B) ) )  @  ( (k2_xcmplx_0 @  ( (k3_xcmplx_0 @  (k20_sin_cos @ A) )  @  (k20_sin_cos @ B) ) )  @  ( (k3_xcmplx_0 @  (k17_sin_cos @ A) )  @  (k17_sin_cos @ B) ) ) ) ) ) ) ) ) , file(complex2, t3_complex2)).