exact ⟨tp, tq, add_lt_add tp tq⟩
case neg.intro.intro.intro.intro.h
R : Type ?u.178489
ι : Type u_2
inst✝² : CommSemiring R
S : Type u_1
inst✝¹ : CommRing S
inst✝ : IsDomain S
p q : MvPolynomial ι S
hp✝ : ¬p.totalDegree = 0
hq✝ : ¬q.totalDegree = 0
this : (p.leadingTerms * q.leadingTerms).totalDegree = p.totalDegree + q.totalDegree
wp : MvPolynomial ι S
hp : p = p.leadingTerms + wp
tp : wp.totalDegree < p.totalDegree
wq : MvPolynomial ι S
hq : q = q.leadingTerms + wq
tq : wq.totalDegree < q.totalDegree
⊢ wp.totalDegree < p.totalDegree ∧
    wq.totalDegree < q.totalDegree ∧ wp.totalDegree + wq.totalDegree < p.totalDegree + q.totalDegree
no goals