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Proof step 9 from proof index-update-adr-in (previous step)

# kx0 = # ax1, ∀ ax0, adr0, ri0. # ax1 = # ax0 → (adr0 ∈ ri0[kx0, ax0] ↔ adr0 ∈ ax0 ∨ adr0 ∈ ri0 \ kx0.toSet) ⊦ adr ∈ ri[key, adr1][kx0, ax1] ↔ adr = adr1 ∨ adr ∈ ax1 ∨ adr ∈ (ri \ kx0.toSet) -- key, dups(kx0), key ∈ kx0

User applied rule all left

And obtained the following new goals

Proof step 10:
# kx0 = # ax1, # ax1 = # ax1 → (adr ∈ ri[key, adr1][kx0, ax1] ↔ adr ∈ ax1 ∨ adr ∈ ri[key, adr1] \ kx0.toSet) ⊦ adr ∈ ri[key, adr1][kx0, ax1] ↔ adr = adr1 ∨ adr ∈ ax1 ∨ adr ∈ (ri \ kx0.toSet) -- key, dups(kx0), key ∈ kx0

Rule argument

pos: left 2 terms: ax1, adr, ri[key, adr1] abort: F discard: T computed: T

Additional information

Used terms: ax1, adr, ri[key, adr1]