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Proof step 35 from proof range-rem-in (previous step)

ri-cons(ri, nodes(gstore, ginval)), key ∈ ri, key0 ∈ ri ⊦ ri[key0] = ri[key], ∃ key1. key1 ∈ ri -- key ∧ (ri -- key)[key1] = ri[key0]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 36:
ri-cons(ri, nodes(gstore, ginval)), key0 ∈ ri, key ∈ ri ⊦ ri[key0] = ri[key], ∃ key1. key1 ∈ ri ∧ ri[key1] = ri[key0]

Rule argument

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s)