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Proof step 3 from proof abs-files-gc-copy (previous step)

# ax = # kx, new(ax, fs), ri-cons(ri, fs), kx.toSet ⊆ dom ri ⊦ dups(kx), dups(ax), (inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory ↔ inodekey(ino) ∈ ri[kx, ax] ∧ ¬ fs[ax, fs[ri[kx]]][ri[kx, ax][inodekey(ino)]].directory) ∧ ( inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)) = mkfile(fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs[ax, fs[ri[kx]]], ri[kx, ax])))

User applied rule case distinction

And obtained the following new goals

Rule argument

pos: right 3

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