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Proof step 20 from proof inv-add3 (previous step)

ro.inodes?, fo.inodes?, log-cons(log, fs), node-cons(nd3.key, nd3), node-cons(nd0.key, nd0), node-cons(nd2.key, nd2), node-cons(fs[adr].key, fs[adr]), ri-cons(ri, fs), ri-inj(ri), ri-inj(fi), adr ∈ log, adr ∈ fs ⊦ adr1 = adr2, adr1 = ri[key], adr2 = ri[key], node-cons(fs[adr1, nd3][adr2, nd0][ri[key], nd2][adr].key, fs[adr1, nd3][adr2, nd0][ri[key], nd2][adr]), ri[key] ∈ fs, adr2 ∈ fs, adr1 ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 21:
⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr]
Proof step 22:
fo.inodes?, ro.inodes?, log-cons(log, fs), node-cons(fs[adr].key, fs[adr]), 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), adr ∈ fs, adr ∈ log ⊦ adr = ri[key], adr1 = ri[key], adr1 = adr2, adr2 = ri[key], node-cons(fs[adr1, nd3][adr2, nd0][adr].key, fs[adr1, nd3][adr2, nd0][adr]), adr1 ∈ fs, adr2 ∈ fs, ri[key] ∈ fs

Rule argument

spec: store, inst: node-store name: At-other seq: ⊦ adr ≠ adr0 → fs[adr0, nd][adr] = fs[adr] subst: [adr, nd, adr0, fs] → [adr, nd2, ri[key], fs[adr1, nd3][adr2, nd0]] flags: <all paths>

Additional information

Used terms: adr, nd2, ri[key], fs[adr1, nd3][adr2, nd0]