"we suppose further" is a correct and usable phrase in written English.
You can use it when you are suggesting a hypothetical situation or presenting a conclusion based on the evidence. For example, "Based on our findings, we suppose further that the impact of the virus on the economy will be long-term."
If we suppose further that is regressive, the Cauchy operator is defined for all.
We suppose further that is a nonnegative function for with in Theorem 2.5.
We suppose further that the agent did what he did because the having of the pro-attitude and belief were states with (respectively) a conative and a cognitive nature, and even more importantly, they are psychological states with certain propositional contents.
We suppose further that either (i) the multiplicity of (lambda omega)) is 1 in some neighborhood (Msubsetmathbf{W}) of ω, or (ii) (lambda omega)) is an eigenvalue of multiplicity (l (l=2, 3, ldots, 2m)) for each (omegain M), (Msubsetmathbf{W}).
We suppose further that either (i) the multiplicity of (lambda omega)) is 1 in some neighborhood (Msubset mathbf{W}) of ω, or (ii) (lambda omega)) is an eigenvalue of multiplicity (l (l=2, 3, ldots, 2m)) for each (omegain M), (Msubset mathbf{W}).
Now we suppose further that the two competitors in (1.1) are under weak competition in the sense that (c(x), e(x)>0) are small such that frac{c(x)}{min_{xinoverline{Omega}}f(x)}< frac{a(x)}{d(x)}, qquad frac{e(x)}{min_{xinoverline{Omega}}b(x)}< frac{d(x)}{a(x)}quad mbox{for all } xinoverline{Omega}.
But we supposed further that delirious mania itself might induce one manic episode or worsen the ongoing mania.
By taking another appropriate subsequence we may suppose further i) lim n ||Px n ||, lim n ||Px n ||2, lim n ||Qx n ||2 exist. .
And suppose further that we know what the due compensation is for having one's forearm broken.
Suppose further that we are able to single out this relation by some sort of act of intellectual attention or abstraction, and that (having done so) we have given it the name "falling under".
Suppose, further, that we think that no bicycle could have been originally composed of just one third of its original parts, even with substitutes for the other two thirds.
