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Proof step 80 from proof fsync-inode-overwrite (previous step)

icache[m] = mkientry(true, mkinode(m2, md, boolvar, m3, m4, m5)), files0[m] = mkfile(m0, md0, m1, content), icache-cons(icache, dirs, files0), m ∈ files0, m ∈ icache, m2 ∈ dirs ∧ m3 = dirs[m2].nlink ∧ m5 = dirs[m2].size ∧ m4 = dirs[m2].nsubdirs ∧ boolvar ∨ m2 ∈ files0 ∧ m3 = files0[m2].nlink ∧ m4 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; icache0 := icache; inode := mkinode(m2, md, boolvar, m3, m4, m5); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files0[inode.ino] = (files0 ⊕ icache0)[inode.ino])

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 81:
files0[m] = mkfile(m0, md0, m1, content), icache[m] = mkientry(true, mkinode(m2, md, boolvar, m3, m4, m5)), files0[m2] = mkfile(m6, md1, m7, content0), icache-cons(icache, dirs, files0), m ∈ icache, m ∈ files0, m2 ∈ dirs ∧ m3 = dirs[m2].nlink ∧ m5 = dirs[m2].size ∧ m4 = dirs[m2].nsubdirs ∧ boolvar ∨ m2 ∈ files0 ∧ m3 = m7 ∧ m4 = 0 ∧ ¬ boolvar ⊦ [fail#(; ; err); asynced := ?; icache0 := icache; inode := mkinode(m2, md, boolvar, m3, m4, m5); if err = ESUCCESS then {asynced := false; icache_set_status#(m, asynced; err, icache)}] (err = ESUCCESS → files0[inode.ino] = (files0 ⊕ icache0)[inode.ino])

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[m2], m6, md1, m7, 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[m2], m6, md1, m7, content0