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Proof step 3 from proof sorted-lt-h (previous step)

m0 < m, m1 < m, sorted(zbrar, n, m) ⊦ zbrar[n + m0].key < zbrar[n + m1].key ↔ m0 < m1

User applied rule structural induction

And obtained the following new goals

Proof step 4:
m1 < m2 +1, m0 < m2 +1, sorted(zbrar, n, m2 +1), ∀ m0, m1, zbrar, n. m0 < m2 ∧ m1 < m2 ∧ sorted(zbrar, n, m2) → (zbrar[n + m0].key < zbrar[n + m1].key ↔ m0 < m1) ⊦ zbrar[n + m0].key < zbrar[n + m1].key ↔ m0 < m1

Rule argument

indvar: m

Additional information

Used simplifier rules: sorted-base: ⊦ sorted(zbrar, n, 0);%nat freely generated by 0, +1;;% ⊦ ¬ m < 0; (s)