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Proof step 2 from proof log-cons-copy-new (previous step)

# kx = # ax, ri-cons(ri, fs), kx.toSet ⊆ dom ri ⊦ dups(ax), dups(kx), log-cons(ax, fs[ax, fs[ri[kx]]])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 3:
# kx = # ax, adr ∈ ax, kx.toSet ⊆ dom ri, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ dups(kx), dups(ax), node-cons(fs[ax, fs[ri[kx]]][adr].key, fs[ax, fs[ri[kx]]][adr])

Rule argument

Additional information

Used simplifier rules: ri-cons: ⊦ ri-cons(ri, fs) ↔ (∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]));%log-cons: ⊦ log-cons(log, fs) ↔ (∀ adr. adr ∈ log → adr ∈ fs ∧ node-cons(fs[adr].key, fs[adr]));%# ax = # ndx ⊦ adr ∈ fs[ax, ndx] ↔ adr ∈ fs ∨ adr ∈ ax; (s)% ⊦ # ri[kx] = # kx; (s)% ⊦ # fs[ax] = # ax; (s)