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Proof step 5 from proof keep-sorted (previous step)

zbr.key = zbrar[n0].key, n0 < # zbrar, ∀ zbr, zbrar, n0, n. zbr.key = zbrar[n0].key ∧ n0 < # zbrar → (sorted(zbrar[n0, zbr], n, m0) ↔ sorted(zbrar, n, m0)) ⊦ sorted(zbrar[n0, zbr], n, m0 + 1) ↔ sorted(zbrar, n, m0 + 1)

User applied rule constructor cut

And obtained the following new goals

Proof step 6:
zbr.key = zbrar[n0].key, m0 = m +1, n0 < # zbrar, ∀ zbr, zbrar, n0, n. zbr.key = zbrar[n0].key ∧ n0 < # zbrar → (sorted(zbrar[n0, zbr], n, m0) ↔ sorted(zbrar, n, m0)) ⊦ sorted(zbrar[n0, zbr], n, m0 + 1) ↔ sorted(zbrar, n, m0 + 1)

Rule argument

var: m0

Additional information

Used simplifier rules: sorted-one: ⊦ sorted(zbrar, n, 1);%nat freely generated by 0, +1;;%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic