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Proof step 1377 from proof refine-truncate (previous step)

abs-dirs(fs0, ri0)[m] = mkdir(m7, md3, m8, m9, entries), fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, # links(m, abs-dirs(fs0, ri0)), 0, m3), abs-files(fs0, ri0)[m, mkfile(m1, md, # links(m, abs-dirs(fs0, ri0)), abs-content(m, fs0, ri0) upto min(m1, m2))] = abs-files (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2])), abs-dirs(fs0, ri0) = abs-dirs (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2]), fs0[ri0[inodekey(ROOT_INO)]].directory, orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(m1, md, # links(m, abs-dirs(fs0, ri0)), abs-content(m, fs0, ri0) upto min(m1, m2))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ri-inj(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(m1, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), datakey(m, n) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(ROOT_INO) ∈ ri0, inodekey(m) ∈ ri0, asynced0 → boolvar0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, n * VFS_PAGE_SIZE < min(m1, m2) → # (abs-content(m, fs0, ri0) upto min(m1, m2))[n] = VFS_PAGE_SIZE ⊦ # (adr1 = ri0[datakey(m, n)] ⊃ truncnode(inodekey(m), min(m1, m2));fs0[ri0[datakey(m, n)]]).data = VFS_PAGE_SIZE, adr1 = adr2, adr2 = ri0[datakey(m, n)], m = 0, orphans (abs-dirs(fs0, ri0), abs-files (fs0[adr1, truncnode(inodekey(m), min(m1, m2))][adr2, inodenode(inodekey(m), md, false, # links(m, abs-dirs(fs0, ri0)), 0, m1)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)), adr1 ∈ fs0, adr2 ∈ fs0, dentrykey(m, name) ∈ ri0, m2 ≤ m1 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 ≤ m1 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?)

Heuristic nonsplitting cut applied rule cut formula

And closed the goal!

Rule argument

fma: adr1 = ri0[datakey(m, n)]

Additional information

Used simplifier rules: ⊦ datakey(m, n) ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → # fs[ri[datakey(m, n)]].data = VFS_PAGE_SIZE; (s)% ⊦ key ∈ ri ∧ ubifs-cons(fs, ri, ro, fi, fo, log) → ri[key] ∈ fs; (ss) Used formulas: adr1 = ri0[datakey(m, n)]