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Proof step 29 from proof inv-gc (previous step)

# kx = # ax, as ∩ range ri0[kx, ax] = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ ax.toSet = ∅, ro.inodes?, fo.inodes?, log-cons(log0, fs0), new(ax, fs0), node-cons(fs0[adr].key, fs0[adr]), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]]), ri-cons(ri0, fs0), ri-inj(ri0), ri-inj(fi), adr ∈ log0, adr ∈ fs0, adr ∈ as, kx.toSet ⊆ dom ri0, ∀ adr. adr ∈ as ∩ log0.toSet ↔ adr ∈ ∅ ⊦ # as = 0, as = ∅, dups(kx), dups(ax)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 30:
# kx = # ax, as ∩ ax.toSet = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ range ri0[kx, ax] = ∅, fo.inodes?, ro.inodes?, log-cons(log0, fs0), new(ax, fs0), node-cons(fs0[adr].key, fs0[adr]), ri-cons(ri0, fs0), ri-cons(ri0[kx, ax], fs0[ax, fs0[ri0[kx]]]), ri-inj(fi), ri-inj(ri0), adr ∈ as, adr ∈ fs0, adr ∈ log0, kx.toSet ⊆ dom ri0, ∀ adr0. ¬ adr0 ∈ as ∩ log0.toSet ⊦ # as = 0, as = ∅, dups(ax), dups(kx)

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ adr ∈ ∅; (s)