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Proof step 10 from proof at-range (previous step)

nused0 < # zbrar, key ∈ key-range(zbrar, 0, nused0 + 1, ri) ⊦ key-range(zbrar, 0, nused0 + 1, ri)[key] = ri[key]

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: <toplevel> name: range-first seq: ⊦ nused ≠ 0 ∧ nused < # zbrar → key-range(zbrar, 0, nused + 1, ri) = ri |≤ zbrar[0].key subst: [ri, nused, zbrar] → [ri, nused0, zbrar] flags: <all paths>

Additional information

Used simplifier rules: range-one: ⊦ key-range(zbrar, 0, 1, ri) = ri;% ⊦ key0 ∈ ri |≤ key1 ↔ key0 ∈ ri ∧ ¬ key1 < key0; (s)% ⊦ ¬ key1 < key0 ∧ key0 ∈ ri → (ri |≤ key1)[key0] = ri[key0]; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: ri, nused0, zbrar