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Proof step 24 from proof inv-gc (previous step)

# kx = # ax, as ∩ range ri0[kx, ax] = ∅, ax.toSet ∩ log0.toSet = ∅, as ∩ 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, kx.toSet ⊆ dom ri0 ⊦ dups(kx), dups(ax), ¬ adr ∈ as ∧ node-cons(fs0[ax, fs0[ri0[kx]]][adr].key, fs0[ax, fs0[ri0[kx]]][adr])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ # ax = # ndx ∧ ¬ adr ∈ ax → fs[ax, ndx][adr] = fs[adr]
Proof step 26:
# kx = # ax, # ax = # fs0[ri0[kx]], as ∩ ax.toSet = ∅, as ∩ log0.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 ∈ fs0, adr ∈ log0, kx.toSet ⊆ dom ri0 ⊦ dups(ax), dups(kx), adr ∈ ax, ¬ adr ∈ as ∧ node-cons(fs0[adr].key, fs0[adr])

Rule argument

spec: aubifs-base name: at-write-other seq: ⊦ # ax = # ndx ∧ ¬ adr ∈ ax → fs[ax, ndx][adr] = fs[adr] subst: [adr, ndx, ax, fs] → [adr, fs0[ri0[kx]], ax, fs0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # fs[ax] = # ax; (s)% ⊦ # ri[kx] = # kx; (s)% ⊦ new(log, fs) ∧ adr ∈ fs → ¬ adr ∈ log; (s) Used terms: adr, fs0[ri0[kx]], ax, fs0