[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 27 from proof ri-cons-copy-new (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ # ax = # ndx ∧ ¬ adr ∈ ax → fs[ax, ndx][adr] = fs[adr]
Proof step 29:
# kx = # ax, new(ax, fs), key ∈ ri, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx), dups(ax), key-cons(key, fs[ax, fs[ri[kx]]][ri[key]]), key ∈ kx, # ax = # fs[ri[kx]] ∧ ¬ ri[key] ∈ ax
Proof step 31:
# kx = # ax, # ax = # fs[ri[kx]], new(ax, fs), key ∈ ri, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx), dups(ax), key-cons(key, fs[ri[key]]), key ∈ kx, ri[key] ∈ 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] → [ri[key], fs[ri[kx]], ax, fs] flags: <all paths>

Additional information

Used terms: ri[key], fs[ri[kx]], ax, fs