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Proof step 6 from proof del-le (previous step)

key ∈ ri ⊦ ((ri -- key0) |≤ key1)[key] = ri[key], key = key0, key1 < key0, key1 < key

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: at-le seq: ⊦ ¬ key1 < key0 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0] subst: [key0, key1, ri] → [key, key1, ri -- key0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ key ≠ key0 → (ri -- key0)[key] = ri[key]; (s)% ⊦ key ∈ ri -- key0 ↔ key ≠ key0 ∧ key ∈ ri; (s) Used terms: key, key1, ri -- key0