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Proof step 59 from proof fsync-inode-overwrite (previous step)

inode1.nlink = files0[inode1.ino].nlink, inode1.nsubdirs = 0, icache[m] = mkientry(true, inode1), files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, inode1.ino ∈ files0, ¬ inode1.directory ⊦ [inode0 := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] ( err = ESUCCESS → (inode0.ino = inode1.ino ⊃ (files0[inode1.ino].meta:= inode1.meta).size:= inode1.size;files0[inode0.ino]) = (files0 ⊕ icache0)[inode0.ino])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 60:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, inode1), ¬ boolvar, err = ESUCCESS, icache0 = icache, inode1 = mkinode(m2, md, boolvar, m3, m4, m5), m3 = files0[m2].nlink, m4 = 0, icache-cons(icache, dirs, files0), m2 ∈ files0, m ∈ icache, m ∈ files0 ⊦ [inode0 := inode1; if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → (inode0.ino = m2 ⊃ (files0[m2].meta:= md).size:= m5;files0[inode0.ino]) = (files0 ⊕ icache0)[inode0.ino])

Rule argument

spec: inode name: elim seq: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2) subst: [inode, m, md, boolvar, m0, m1, m2] → [inode1, m2, md, boolvar, m3, m4, m5]

Additional information

Used simplifier rules: ⊦ ( ( ( (m = inode.ino ∧ md = inode.meta) ∧ (boolvar ↔ inode.directory)) ∧ m0 = inode.nlink) ∧ m1 = inode.nsubdirs) ∧ m2 = inode.size ↔ inode = mkinode(m, md, boolvar, m0, m1, m2); (elim) Used terms: inode1, m2, md, boolvar, m3, m4, m5