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Proof step 956 from proof refine-truncate (previous step)

abs-files(fs0, ri0)[m] = mkfile(m0, md1, m3, content0), fs0[ri0[inodekey(m)]] = inodenode(key0, md0, false, m1, 0, m4), dirs = abs-dirs(fs0, ri0), files = abs-files(fs0, ri0)[m, mkfile(m0, md1, m3, content0 upto m2)], ino = inode.ino, inode = mkinode(m, md, false, m1, 0, n0), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ri-inj(fi), ri-inj(ri0), ri-inj(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, ino ∈ files, m2 ≤ n0, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, m = 0, buf-opt0.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, m2 / VFS_PAGE_SIZE ∈ content0, ∃ asynced. afs-cons(dirs, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta]) → dirs = abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2]) ∧ files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta] = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])) ∧ orphans (abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2]), abs-files(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0)) ∧ (asynced → boolvar4) ∧ mkinode(m, md, false, m1, 0, n0) = (m ∈ dirs ⊃ mkinode(m, dirs[m].meta, true, dirs[m].nlink, dirs[m].nsubdirs, dirs[m].size) ;mkinode (m, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].meta, false, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].nlink, 0, files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta][m].size) ) ∧ ESUCCESS = ESUCCESS

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 957:
fs0[ri0[inodekey(m)]] = inodenode(key0, md0, false, m1, 0, m4), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m1, abs-content(m, fs0, ri0) upto m2)]), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0)), replay-cons-strong(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ri-inj(fi), ri-inj(ri0), ri-inj(ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, m2 ≤ n0, asynced0 → boolvar0 ⊦ m2 % VFS_PAGE_SIZE = 0, adr1 = adr2, m = 0, buf-opt0.some?, adr2 ∈ fs0, adr1 ∈ fs0, datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0, abs-dirs(fs0, ri0) = abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2]) ∧ abs-files(fs0, ri0)[m, mkfile(n0, md, m1, abs-content(m, fs0, ri0) upto m2)] = abs-files (fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), m2, ri0[inodekey(m), adr2])) ∧ orphans (abs-dirs(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2]), abs-files(fs0[adr1, truncnode(inodekey(m), m2)][adr2, inodenode(inodekey(m), md, false, m1, 0, n0)], ri0[inodekey(m), adr2])) = abs-keys(orphans(fs0, ri0))

Rule argument

Additional information

Used simplifier rules: ⊦ n ∈ abs-content(ino, fs, ri) ↔ datakey(ino, n) ∈ ri; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).directory ↔ boolvar; (s)% ⊦ inodenode(key, md, boolvar, m, m0, m1).nlink = m; (s)% ⊦ mkfile(m, md, m0, content).size = m; (s)% ⊦ mkfile(m, md, m0, content).nlink = m0; (s)% ⊦ mkfile(m, md, m0, content).meta = md; (s)%⊦ ino ∈ abs-dirs(fs, ri) ↔ inodekey(ino) ∈ ri ∧ fs[ri[inodekey(ino)]].directory; (s)% ⊦ mkfile(m, md, m0, content).meta:= md0 = mkfile(m, md0, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).meta = md; (s)% ⊦ files[ino, af][ino, af0] = files[ino, af0]; (s)% ⊦ mkfile(m, md, m0, content).size:= m1 = mkfile(m1, md, m0, content); (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).size = m2; (s)% ⊦ files[ino, af][ino0] = (ino0 = ino ∧ ino ∈ files ⊃ af;files[ino0]); (s)%⊦ mkfile(m, md, m0, content) = mkfile(m1, md0, m2, content0) ↔ m = m1 ∧ md = md0 ∧ m0 = m2 ∧ content = content0; (ws)%⊦ abs-file(ino, fs, ri) = mkfile (fs[ri[inodekey(ino)]].size, fs[ri[inodekey(ino)]].meta, fs[ri[inodekey(ino)]].nlink, abs-content(ino, fs, ri)); (s)%⊦ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory → abs-files(fs, ri)[ino] = abs-file(ino, fs, ri); (s)%⊦ ino ∈ abs-files(fs, ri) ↔ inodekey(ino) ∈ ri ∧ ¬ fs[ri[inodekey(ino)]].directory; (s)% ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (s)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)