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Proof step 8 from proof crash-neutral-add2 (previous step)

fs0 = fs, log0 = log, fo.inodes?, ro.inodes?, log-cons(log, fs), node-cons(nd1.key, nd1), node-cons(nd2.key, nd2), ri-cons(ri, fs), ri-inj(fi), ri-inj(ri) ⊦ (∀ adr1, adr2. ¬(new(adr1 ' + adr2 ', fs) ∧ ¬ dups(adr1 ' + adr2 '))) ∧ ⟨err := ENOSPC; boolvar := ?⟩ (boolvar ∧ fs0 = fs ∧ log0 = log), ∃ adr1, adr2. (new(adr1 ' + adr2 ', fs) ∧ ¬ dups(adr1 ' + adr2 ')) ∧ ⟨adr0 := adr1, adr := adr2; fs := fs[adr0, nd2][adr, nd1], log := (log + adr0) + adr, err := ESUCCESS; boolvar := ?⟩ (boolvar ∧ fs0 = fs ∧ log0 = log), ⟨fail#(; ; err); 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(nd2.key, nd2), node-cons(nd1.key, nd1), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi) ⊦ ⟨fail#(; ; err); adr0 := ?, adr := ?; boolvar := ?⟩ boolvar, (adr ∈ fs ∨ adr0 ∈ fs ∨ adr = adr0) ∧ ⟨err := ENOSPC; boolvar := ?⟩ boolvar, ∃ adr1, adr2. ¬ adr1 ∈ fs ∧ ¬ adr2 ∈ fs ∧ adr1 ≠ adr2 ∧ ⟨adr0 := adr1, adr := adr2; fs1 := fs[adr0, nd2][adr, nd1], log1 := (log + adr0 ') + adr ', err := ESUCCESS; boolvar := ?⟩ (boolvar ∧ fs = fs1 ∧ log = log1)

Rule argument

Additional information

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