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Proof step 114 from proof eq-io-truncate (previous step)

VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m3, md1, m4, content), files[ino, files[ino].size:= inode.size][ino, files[ino, files[ino].size:= inode.size][ino].meta:= inode.meta] = files0, dirs = dirs1, dirs = dirs0, files = files1, files1 = files2[m, mkfile(m3, md1, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)], ino = inode.ino, inode = mkinode(m, md, false, m4, 0, n0), inode0 = mkinode(m, md, false, m4, 0, m2), m2 / VFS_PAGE_SIZE ∈ content, m ∈ files2, ino ∈ files, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], m2 ≤ n0 ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode0, boolvar1, err, dirs1, files2, boolvar2)⟩ ( buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ inode0 = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar1 ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files2 = files0), m2 % VFS_PAGE_SIZE = 0, buf-opt.some?

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 115:
VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files2[m] = mkfile(m3, md1, m4, content), files2[m, mkfile(n0, md, m4, content[m2 / VFS_PAGE_SIZE, fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)] = files0, dirs0 = dirs1, inode0 = mkinode(m, md, false, m4, 0, m2), m2 % VFS_PAGE_SIZE ≠ 0, m2 / VFS_PAGE_SIZE ∈ content, m ∈ files2, m2 ≤ n0, VFS_PAGE_SIZE ≤ # content[m2 / VFS_PAGE_SIZE], ¬ buf-opt.some? ⊦ ⟨afs_truncate#(n0, m2 / VFS_PAGE_SIZE; buf-opt, inode0, boolvar1, err, dirs1, files2, boolvar2)⟩ ( buf-opt = some(fill(content[m2 / VFS_PAGE_SIZE], zero, m2 % VFS_PAGE_SIZE, n1)) ∧ inode0 = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size) ;mkinode(m, files0[m].meta, false, files0[m].nlink, 0, files0[m].size) ) ∧ boolvar1 ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files2 = files0)

Rule argument

Additional information

Used simplifier rules: ⊦ ino ∈ files[ino0, af] ↔ ino ∈ files; (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)% ⊦ mkinode(m, md, boolvar, m0, m1, m2).ino = m; (s)