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Proof step 100 from proof fsync-inode-overwrite (previous step)

files0[m] = mkfile(m0, md0, m1, content), err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m ∈ icache, m ∈ files0, ¬ icache[m].dirty ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → mkfile(m0, md0, m1, content) = (files0 ⊕ icache0)[m])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 101:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(boolvar, inode), ¬ boolvar, err = ESUCCESS, icache0 = icache, icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache ⊦ [icache_set_status#(m, false; err, icache)] (err = ESUCCESS → mkfile(m0, md0, m1, content) = (files0 ⊕ icache0)[m])

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[m], boolvar, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[m], boolvar, inode