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Proof step 18 from proof keep-sorted (previous step)

zbr.key = zbrar[n0].key, n < # zbrar, n0 < # zbrar, sorted(zbrar[n0, zbr], n + 1, m + 1), sorted(zbrar, n + 1, m + 1) ⊦ zbrar[n].key < zbrar[n0, zbr][n + 1].key ↔ zbrar[n].key < zbrar[n + 1].key, n = n0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array, inst: zbranch-array name: Put-other seq: ⊦ m ≠ n → zbrar[n, zbr][m] = zbrar[m] subst: [m, zbr, n, zbrar] → [n + 1, zbr, n0, zbrar] flags: <all paths>

Additional information

Used simplifier rules: ⊦ m = m + n ↔ n = 0; (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: n + 1, zbr, n0, zbrar