Let x be given.
Assume Hx Hxpos.
Apply SNoLtLe_or 0 (recip_SNo_pos x) SNo_0 (SNo_recip_SNo_pos x Hx Hxpos) to the current goal.
Assume H1: 0 < recip_SNo_pos x.
An exact proof term for the current goal is H1.
Assume H1: recip_SNo_pos x ≤ 0.
We will prove False.
Apply SNoLt_irref 0 to the current goal.
We will prove 0 < 0.
Apply SNoLtLe_tra 0 1 0 SNo_0 SNo_1 SNo_0 SNoLt_0_1 to the current goal.
We will prove 1 ≤ 0.
rewrite the current goal using recip_SNo_pos_invR x Hx Hxpos (from right to left).
We will prove x * recip_SNo_pos x ≤ 0.
rewrite the current goal using mul_SNo_zeroR x Hx (from right to left).
We will prove x * recip_SNo_pos x ≤ x * 0.
An exact proof term for the current goal is nonneg_mul_SNo_Le x (recip_SNo_pos x) 0 Hx (SNoLtLe 0 x Hxpos) (SNo_recip_SNo_pos x Hx Hxpos) SNo_0 H1.
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