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Proof step 11 from proof log-cons-copy-new (previous step)

# kx1 = # ax1, # kx = # ax0, key0 ∈ ri, kx1.toSet ⊆ dom ri, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(ax0), dups(ax1), dups(ax1 + ax0), dups(kx1 + kx), dups(kx1), dups(kx), node-cons(fs[ax1, fs[ri[kx1]]][adr, fs[ri[key0]]][ax0, fs[ri[kx]]][adr].key, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key0]]][ax0, fs[ri[kx]]][adr]), adr ∈ ax0, adr ∈ ax1, key0 ∈ kx1, key0 ∈ kx

User applied rule insert rewrite lemma

And obtained the following new goals

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, fs[ri[kx]], ax0, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key0]]]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # fs[ax] = # ax; (s)% ⊦ # ri[kx] = # kx; (s) Used terms: adr, fs[ri[kx]], ax0, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key0]]]