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Proof step 68 from proof eq-io-truncate (previous step)

# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, m1, content0), dirs0 = dirs1, files1 = files[m, mkfile(m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE)] upto m2)], m2 % VFS_PAGE_SIZE ≠ 0, buf-opt.some?, m ∈ files, m2 ≤ n0 ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files1); inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE - m2 % VFS_PAGE_SIZE) = fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m1, 0, n0)) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 69:
# buf-opt.buf = VFS_PAGE_SIZE, VFS_PAGE_SIZE = n1 + m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE = n2 + m2 % VFS_PAGE_SIZE, files[m] = mkfile(m0, md0, m1, content0), dirs0 = dirs1, files1 = files[m, mkfile(m0, md0, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n2)] upto m2)], buf-opt.some?, m ∈ files, m2 ≤ n0, m2 % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ ⟨afs_inode_sync#(mkinode(m, md, false, m1, 0, n0); dirs1, files1); inode := (m ∈ dirs1 ⊃ mkinode(m, dirs1[m].meta, true, dirs1[m].nlink, dirs1[m].nsubdirs, dirs1[m].size) ;mkinode(m, files1[m].meta, false, files1[m].nlink, 0, files1[m].size) ); err := ESUCCESS; asynced := ?⟩ ( fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n2) = fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1) ∧ inode = (m ∈ dirs0 ⊃ mkinode(m, dirs0[m].meta, true, dirs0[m].nlink, dirs0[m].nsubdirs, dirs0[m].size);mkinode(m, md, false, m1, 0, n0)) ∧ err = ESUCCESS ∧ dirs1 = dirs0 ∧ files1 = files[m, mkfile(n0, md, m1, content0[m2 / VFS_PAGE_SIZE, fill(buf-opt.buf, zero, m2 % VFS_PAGE_SIZE, n1)] upto m2)]), m2 % VFS_PAGE_SIZE = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n]

Additional information

Used simplifier rules: ⊦ VFS_PAGE_SIZE ≠ 0; (s)%n ≠ 0 ⊦ m % n ≤ n; (s)%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: m2 % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n