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Proof step 24 from proof keep-range (previous step)

zbr.key = zbrar[m].key, 2 + m0 < nused, m < # zbrar, m0 + 1 < nused, 2 + m0 < # zbrar, m0 + 1 < # zbrar, nused ≤ # zbrar ⊦ (ri |> zbrar[m, zbr][m0].key) |≤ zbrar[m, zbr][m0 + 1].key = (ri |> zbrar[m0].key) |≤ zbrar[m0 + 1].key

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ m ≠ n → zbrar[n, zbr][m] = zbrar[m]
Proof step 26:
zbr.key = zbrar[m].key, m0 + 1 < # zbrar, 2 + m0 < # zbrar, m0 + 1 < nused, m < # zbrar, 2 + m0 < nused, nused ≤ # zbrar ⊦ m0 + 1 = m, (ri |> zbrar[m, zbr][m0].key) |≤ zbrar[m0 + 1].key = (ri |> zbrar[m0].key) |≤ zbrar[m0 + 1].key

Rule argument

spec: array, inst: zbranch-array name: Put-other seq: ⊦ m ≠ n → zbrar[n, zbr][m] = zbrar[m] subst: [m, zbr, n, zbrar] → [m0 + 1, zbr, m, zbrar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ zbrar[m + 1, zbr][m] = zbrar[m]; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < # zbrar → zbrar[m, zbr][m] = zbr; (s) Used terms: m0 + 1, zbr, m, zbrar