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Proof step 45 from proof write-inode-inv (previous step)

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, ⌊err0⌋ ⊦ write-inv(0, n1, mkinode(ino, md, false, m1, 0, files0[ino].size), buf, n, dirs, files0, files1)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 46:
files1[ino] = mkfile(m, md, m1, content), files0[ino] = mkfile(m2, md0, m3, content0), write-inv(0, n1, mkinode(ino, md, false, m1, 0, m0), buf, n, dirs, files0, files1), ino ∈ files1, ⌊err0⌋ ⊦ write-inv(0, n1, mkinode(ino, md, false, m1, 0, m2), buf, n, dirs, files0, files1)

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] → [files0[ino], m2, md0, m3, content0]

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: files0[ino], m2, md0, m3, content0