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Proof step 8 from proof restrict-le2 (previous step)

key < key0, key1 < key0, key ∈ ri ⊦ (ri |≤ key0 |≤ key1)[key] = ri[key], 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: in-le: ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0;%at-le-lt: ⊦ key0 < key1 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0];%transitivity: ⊦ key < key0 ∧ key0 < key1 → key < key1; (forward) from specification oelem[key-order] Used terms: key, key1, ri |≤ key0