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Proof step 12 from proof keep-range (previous step)

zbr.key = zbrar[m].key, nused0 < # zbrar, m < # zbrar, nused0 < # zbrar[m, zbr] ⊦ nused0 = 0, ri |≤ zbrar[m, zbr][0].key = key-range(zbrar, 0, nused0 + 1, ri)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
zbr.key = zbrar[m].key, m < # zbrar, nused0 < # zbrar ⊦ nused0 = 0, ri |≤ zbrar[m, zbr][0].key = ri |≤ zbrar[0].key

Rule argument

Additional information

Used simplifier rules: range-first: ⊦ nused ≠ 0 ∧ nused < # zbrar → key-range(zbrar, 0, nused + 1, ri) = ri |≤ zbrar[0].key;% ⊦ # zbrar[n, zbr] = # zbrar; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic