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Proof step 19 from proof ri-cons-copy-new (previous step)

# kx0 = # ax, # ax1 = # kx1, new(ax, fs), new(ax1, fs), key ∈ ri, kx0.toSet ⊆ dom ri, kx1.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(ax), dups(ax1), dups(ax1 + ax), dups(kx1 + kx0), dups(kx1), dups(kx0), key-cons(key, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key]]][ax, fs[ri[kx0]]][adr]), adr ∈ ax1, adr ∈ ax, key ∈ kx1, key ∈ kx0, adr ∈ fs

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ # ax = # ndx ∧ ¬ adr ∈ ax → fs[ax, ndx][adr] = fs[adr]
Proof step 21:
# ax1 = # kx1, # kx0 = # ax, # ax = # fs[ri[kx0]], new(ax1, fs), new(ax, fs), key ∈ ri, kx1.toSet ⊆ dom ri, kx0.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx0), dups(kx1), dups(kx1 + kx0), dups(ax1 + ax), dups(ax1), dups(ax), key-cons(key, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key]]][adr]), adr ∈ fs, key ∈ kx0, key ∈ kx1, adr ∈ ax1, adr ∈ ax

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[kx0]], ax, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key]]]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ # fs[ax] = # ax; (s)% ⊦ # ri[kx] = # kx; (s) Used terms: adr, fs[ri[kx0]], ax, fs[ax1, fs[ri[kx1]]][adr, fs[ri[key]]]