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Proof step 18 from proof write-inode-inv (previous step)

write-inv(0, n1, mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, m0), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ write-inv (0, n1, mkinode(ino, files1[ino].meta, false, files1[ino].nlink, 0, m0 + n), buf, n, dirs, files0[ino, files0[ino].size:= (m0 + n)], files1[ino, (files1[ino].meta:= files1[ino].meta).size:= (m0 + n)])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
files1[ino] = mkfile(m, md, m1, content), write-inv(0, n1, mkinode(ino, md, false, m1, 0, m0), buf, n, dirs, files0, files1), ino ∈ files1 ⊦ write-inv (0, n1, mkinode(ino, md, false, m1, 0, m0 + n), buf, n, dirs, files0[ino, files0[ino].size:= (m0 + n)], files1[ino, (files1[ino].meta:= md).size:= (m0 + n)])

Rule argument

spec: abstract-file name: elim seq: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content) subst: [af, m, md, m0, content] → [files1[ino], m, md, m1, content]

Additional information

Used simplifier rules: ⊦ ((m = af.size ∧ md = af.meta) ∧ m0 = af.nlink) ∧ content = af.content ↔ af = mkfile(m, md, m0, content); (elim) Used terms: files1[ino], m, md, m1, content