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Proof step 8 from proof crash-neutral-add3 (previous step)

fs0 = fs, log0 = log, fo.inodes?, ro.inodes?, log-cons(log, fs), node-cons(nd2.key, nd2), node-cons(nd0.key, nd0), node-cons(nd3.key, nd3), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri) ⊦ (∀ adr1, adr2, adr3. ¬(new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 '))) ∧ ⟨err := ENOSPC; boolvar := ?⟩ (boolvar ∧ fs0 = fs ∧ log0 = log), ∃ adr1, adr2, adr3. (new(adr1 ' + (adr2 ' + adr3), fs) ∧ ¬ dups(adr1 ' + adr2 ' + adr3 ')) ∧ ⟨adr4 := adr1, adr0 := adr2, adr := adr3; fs := fs[adr4, nd3][adr0, nd0][adr, nd2], log := ((log + adr4) + adr0) + adr, err := ESUCCESS; boolvar := ?⟩ (boolvar ∧ fs0 = fs ∧ log0 = log), ⟨fail#(; ; err); adr4 := ?, adr0 := ?, adr := ?; boolvar := ?⟩ boolvar

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
ro.inodes?, fo.inodes?, log-cons(log, fs), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi) ⊦ ⟨fail#(; ; err); adr4 := ?, adr0 := ?, adr := ?; boolvar := ?⟩ boolvar, (adr ∈ fs ∨ adr0 ∈ fs ∨ adr1 ∈ fs ∨ adr = adr0 ∨ adr = adr1 ∨ adr0 = adr1) ∧ ⟨err := ENOSPC; boolvar := ?⟩ boolvar, ∃ adr2, adr3, adr5. ¬ adr2 ∈ fs ∧ ¬ adr3 ∈ fs ∧ ¬ adr5 ∈ fs ∧ adr2 ≠ adr3 ∧ adr2 ≠ adr5 ∧ adr3 ≠ adr5 ∧ ⟨adr4 := adr2, adr0 := adr3, adr := adr5; fs1 := fs[adr4, nd3][adr0, nd0][adr, nd2], log1 := ((log + adr4 ') + adr0 ') + adr ', err := ESUCCESS; boolvar := ?⟩ (boolvar ∧ fs = fs1 ∧ log = log1)

Rule argument

Additional information

Used simplifier rules: ⊦ dups(adr ' + adr0 ') ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' ↔ adr = adr0; (s)% ⊦ adr ∈ adr0 ' + ax ↔ adr = adr0 ∨ adr ∈ ax; (s)% ⊦ dups(adr ' + ax) ↔ adr ∈ ax ∨ dups(ax); (s)% ⊦ new(adr ', fs) ↔ ¬ adr ∈ fs; (s)% ⊦ new(adr ' + log, fs) ↔ ¬ adr ∈ fs ∧ new(log, fs); (s)%a: ⊦ (ax + ax0) + ax1 = ax + ax0 + ax1; from specification list[address-list-set]% ⊦ ax + adr = ax + adr '; (s)