The phrase "assumption would become" is correct and usable in written English.
It can be used when discussing a hypothetical situation where an assumption is expected to change or evolve into something else.
Example: "If the data trends continue, the assumption would become a widely accepted theory in the scientific community."
Alternatives: "assumption might turn into" or "assumption could evolve into".
From then on, Reagan was aided in media coverage, fund-raising and party organization by the assumption that he would become the nominee.
The law squeezed nearly $500 billion out of Medicare over 10 years, trimming payments to providers on the assumption that they would become more productive.
William left Normandy to Robert, and the custody of England was given to William's second surviving son, also called William, on the assumption that he would become king.
The most colossal relics of the U.S. invasion of Iraq will be the outsize military bases the Bush administration began erecting not long after the invasion, under the never explicitly stated assumption that Iraq would become the long-term staging area for U.S. forces in the region.
By properly reclassifying exposure (per our assumption), the rates would become 245/(39,026–5,740) = 7.4 per 1,000 person-years for metformin and 162/(16,700+5,740) = 7.2 per 1,000 person-years for sulfonylureas, resulting in a corrected crude rate ratio of 1.0.
And the assumption was that he would become politically engaged, himself.
And he offered a further rationale for the retrenchment, based on an assumption that the world would become more peaceful.
Lurking beneath firms' commitments and resources to sustainability was an assumption that the world would become sustainable as more and more firms reduced their relative burdens.
The OPLC chief executive, Andrew Altman, said that despite the widespread assumption that West Ham would become the main tenant in the stadium following the collapse of the previous process, they would have to table a competitive bid.
Despite the lack of evidence, there has been the unstated assumption that protein thiols would become more oxidized upon aging in parallel with other markers of oxidative damage.
