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Proof step 11 from proof read-loop-err (previous step)

buf = mkbuf(VFS_PAGE_SIZE), err = ESUCCESS, VFS_PAGE_SIZE - (ino2 + ino0) % VFS_PAGE_SIZE ≠ 0, ino1 ≠ ino2 + ino0, m2 ≠ ino2 + ino0, ino2 + ino0 < ino1, ino2 + ino0 < m2 ⊦ [afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), (ino2 + ino0) / VFS_PAGE_SIZE, dirs, files, asynced; buf, err); if err = ESUCCESS then {buf0 := copy (buf, (ino2 + ino0) % VFS_PAGE_SIZE, buf0, ino0, min(ino1 - ino2 + ino0, VFS_PAGE_SIZE - (ino2 + ino0) % VFS_PAGE_SIZE, m2 - ino2 + ino0)); ino3 := ino0 + min(ino1 - ino2 + ino0, VFS_PAGE_SIZE - (ino2 + ino0) % VFS_PAGE_SIZE, m2 - ino2 + ino0)}] (⌊err⌋ ∨ err = ESUCCESS)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 12:
VFS_PAGE_SIZE = n0 + (ino2 + ino0) % VFS_PAGE_SIZE, buf = mkbuf(VFS_PAGE_SIZE), err = ESUCCESS, ino2 + ino0 < m2, ino2 + ino0 < ino1, (ino2 + ino0) % VFS_PAGE_SIZE ≤ VFS_PAGE_SIZE ⊦ [afs_readpage#(mkinode(m, md, boolvar, m0, m1, m2), (ino2 + ino0) / VFS_PAGE_SIZE, dirs, files, asynced; buf, err); if err = ESUCCESS then {buf0 := copy(buf, (ino2 + ino0) % VFS_PAGE_SIZE, buf0, ino0, min(ino1 - ino2 + ino0, n0, m2 - ino2 + ino0)); ino3 := ino0 + min(ino1 - ino2 + ino0, n0, m2 - ino2 + ino0)}] (⌊err⌋ ∨ err = ESUCCESS), ino1 = ino2 + ino0, m2 = ino2 + ino0, n0 = 0

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [(ino2 + ino0) % 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: (ino2 + ino0) % VFS_PAGE_SIZE, VFS_PAGE_SIZE, n