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Proof step 1409 from proof refine-truncate (previous step)

fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), fo.inodes?, orphans(fs0, ri0).inodes?, afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))]), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons (abs-dirs(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), log-cons(log0, fs0), orphans-cons(fs0, ri0, orphans(fs0, ri0)), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, 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), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, 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), min(n0, m2), ri0[inodekey(m), adr2])), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), inodekey(m) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m1) ∈ ri0, inodekey(m1) ∈ ri0[inodekey(m), adr2], buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE, asynced0 → boolvar0 ⊦ fs0[ri0[inodekey(m1)]].nlink = 0 ↔ inodekey(m1) ∈ ri0[inodekey(m), adr2] ∧ (adr2 = ri0[inodekey(m1)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = ri0[inodekey(m1)] ⊃ truncnode(inodekey(m), min(n0, m2));fs0[ri0[inodekey(m1)]]) ) .nlink = 0, adr1 = adr2, m = 0, m1 = m, m1 = ROOT_INO, adr2 ∈ fs0, adr1 ∈ fs0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?), m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 1410:
fs0[ri0[inodekey(m)]] = inodenode(key, md0, false, m0, 0, m3), orphans(fs0, ri0).inodes?, fo.inodes?, afs-cons (abs-dirs(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2]), abs-files(fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2])), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)), afs-cons(abs-dirs(fs0, ri0), abs-files(fs0, ri0)[m, mkfile(n0, md, m0, abs-content(m, fs0, ri0) upto min(n0, m2))]), file-node-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2])), file-node-cons(fs0, ri0), log-cons(log0, fs0), orphans-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0)), orphans-cons(fs0, ri0, orphans(fs0, ri0)), replay-cons-strong (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, 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(n0, m2), ri0[inodekey(m), adr2])), ri-inj(ri0), ri-inj(fi), ubifs-cons (fs0[adr1, truncnode(inodekey(m), min(n0, m2))][adr2, inodenode(inodekey(m), md, false, m0, 0, n0)], ri0[inodekey(m), adr2] \ datakeys(inodekey(m), min(n0, m2), ri0[inodekey(m), adr2]), orphans(fs0, ri0), fi, fo, (log0 + adr1 ') + adr2 '), ubifs-cons(fs0, ri0, orphans(fs0, ri0), fi, fo, log0), inodekey(m1) ∈ ri0, ri0[inodekey(m)] ∈ fs0, inodekey(m) ∈ ri0, asynced0 → boolvar0, buf-opt0.some? → # buf-opt0.buf = VFS_PAGE_SIZE ⊦ fs0[ri0[inodekey(m1)]].nlink = 0 ↔ (adr2 = ri0[inodekey(m1)] ⊃ inodenode(inodekey(m), md, false, m0, 0, n0) ;(adr1 = ri0[inodekey(m1)] ⊃ truncnode(inodekey(m), min(n0, m2));fs0[ri0[inodekey(m1)]]) ) .nlink = 0, adr1 = adr2, m = 0, m1 = ROOT_INO, m1 = m, adr1 ∈ fs0, adr2 ∈ fs0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0, m2 ≤ n0 ∧ m2 % VFS_PAGE_SIZE ≠ 0 ∧ (datakey(m, m2 / VFS_PAGE_SIZE) ∈ ri0 ∨ buf-opt0.some?)

Rule argument

Additional information

Used simplifier rules: ⊦ inodekey(m) = inodekey(m0) ↔ m = m0; (s)% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (las)