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Proof step 17 from proof index-update-dom (previous step)

# ax0 = # ax1, key ∈ ri, ri[key] ∈ ax0, ∀ key. key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ fs[ri[key]].key ∈ ri

User applied rule all left

And obtained the following new goals

Proof step 18:
# ax0 = # ax1, ri[key] ∈ ax0, key ∈ ri, key ∈ ri → ri[key] ∈ fs ∧ key-cons(key, fs[ri[key]]) ⊦ fs[ri[key]].key ∈ ri

Rule argument

pos: left 4 terms: key abort: F discard: T computed: T

Additional information

Used terms: key