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Proof step 84 from proof fsync-inode-others-unchanged (previous step)

files0[m0] = mkfile(m4, md0, m5, content), icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), dirs[m0] = mkdir(m6, md1, m7, m8, entries), icache-cons(icache0, dirs, files0), m ∈ icache0, ⌊err0⌋ , m0 ∈ dirs ∧ m1 = m7 ∧ m3 = m6 ∧ m2 = m8 ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ m0 = m

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 85:
⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ;valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) ))
Proof step 86:
dirs[m0] = mkdir(m6, md1, m7, m8, entries), icache0[m] = mkientry(true, mkinode(m0, md, boolvar, m1, m2, m3)), files0[m0] = mkfile(m4, md0, m5, content), m ∈ icache0, ⌊err0⌋ , ∀ ino. ino ∈ icache0 → icache0[ino].inode.ino = ino ∧ (icache0[ino].dirty ⊃ valid-file-inode(icache0[ino].inode, dirs, files0) ;valid-ino(ino, dirs, files0) ∧ valid-inode(icache0[ino].inode, dirs, files0) ), m0 ∈ dirs ∧ m1 = m7 ∧ m3 = m6 ∧ m2 = m8 ∧ boolvar ∨ m0 ∈ files0 ∧ m1 = m5 ∧ m2 = 0 ∧ ¬ boolvar ⊦ m0 = m

Rule argument

spec: cache-base name: icache-cons seq: ⊦ icache-cons(icache, dirs, files) ↔ (∀ ino. ino ∈ icache → icache[ino].inode.ino = ino ∧ (icache[ino].dirty ⊃ valid-file-inode(icache[ino].inode, dirs, files) ; valid-ino(ino, dirs, files) ∧ valid-inode(icache[ino].inode, dirs, files) )) subst: [files, dirs, icache] → [files0, dirs, icache0] flags: <all paths>

Additional information

Used terms: files0, dirs, icache0