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Proof step 24 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(kx), dups(ax), key ∈ kx, (ri[key] ∈ fs ∨ ri[key] ∈ ax) ∧ key-cons(key, fs[ax, fs[ri[kx]]][ri[key]])

User applied rule case distinction

And obtained the following new goals

Proof step 25:
# 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 ∈ kx, ri[key] ∈ fs, ri[key] ∈ ax
Proof step 27:
# 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

Rule argument

pos: right 4

Proof step 24 from proof ri-cons-copy-new (previous step)

User applied rule case distinction

And obtained the following new goals

Rule argument

Additional information