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Proof step 7 from proof ri-closed-gc (previous step)

# kx0 = # ax1, new(ax1, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), key ∈ ri, kx0.toSet ⊆ dom ri, ∀ ax0, fs0, ri0, ro0. # ax1 = # ax0 ∧ new(ax0, fs0) ∧ ri-closed(ri0, fs0, ro0) ∧ ri-cons(ri0, fs0) ∧ kx0.toSet ⊆ dom ri0 → dups(ax0) ∨ ri-closed(ri0[kx0, ax0], fs0[ax0, fs0[ri0[kx0]]], ro0) ⊦ dups(kx0), dups(ax1), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[ri[kx0]]], ro), adr ∈ fs, key ∈ kx0, adr ∈ ax1

User applied rule all left

And obtained the following new goals

Proof step 8:
# kx0 = # ax1, new(ax1, fs), ri-closed(ri, fs, ro), ri-cons(ri, fs), key ∈ ri, kx0.toSet ⊆ dom ri, # ax1 = # ax1 ∧ new(ax1, fs[adr, fs[ri[key]]]) ∧ ri-closed(ri[key, adr], fs[adr, fs[ri[key]]], ro) ∧ ri-cons(ri[key, adr], fs[adr, fs[ri[key]]]) ∧ kx0.toSet ⊆ dom ri[key, adr] → dups(ax1) ∨ ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[adr, fs[ri[key]]][ri[key, adr][kx0]]], ro) ⊦ dups(ax1), dups(kx0), ri-closed(ri[key, adr][kx0, ax1], fs[adr, fs[ri[key]]][ax1, fs[ri[kx0]]], ro), adr ∈ ax1, key ∈ kx0, adr ∈ fs

Rule argument

pos: left 7 terms: ax1, fs[adr, fs[ri[key]]], ri[key, adr], ro abort: F discard: T computed: F

Additional information

Used terms: ax1, fs[adr, fs[ri[key]]], ri[key, adr], ro