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Proof step 5 from proof drop-gt (previous step)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 6:
⊦ key1 < key0, (key ∈ ri ∧ key1 < key → key ∈ ri[key0, adr]) ∧ (key ∈ ri[key0, adr] ∧ key1 < key → ri[key0, adr][key] = (ri |> key1)[key])

Rule argument

Additional information

Used simplifier rules: in-gt: ⊦ key0 ∈ ri |> key1 ↔ key0 ∈ ri ∧ key1 < key0;%at-gt: ⊦ key1 < key0 ∧ key0 ∈ ri → (ri |> key1)[key0] = ri[key0];% ⊦ key ∈ ri[key0, adr] ↔ key = key0 ∨ key ∈ ri; (ws)