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Proof step 3 from proof sorted-branch-lt-post (previous step)

zbrar[n + m1] = mkzbranch(key, adr, r), m1 < m, sorted(zbrar, n, m) ⊦ zbrar[n].key < key ↔ 0 ≠ m1

User applied rule apply lemma

And obtained the following new goals

Proof step 4:
⊦ m1 < m ∧ sorted(zbrar, n, m) → (zbrar[n].key < zbrar[n + m1].key ↔ 0 ≠ m1)
Proof step 5:
zbrar[n + m1] = mkzbranch(key, adr, r), m1 < m, sorted(zbrar, n, m), m1 < m ∧ sorted(zbrar, n, m) → (zbrar[n].key < zbrar[n + m1].key ↔ 0 ≠ m1) ⊦ zbrar[n].key < key ↔ 0 ≠ m1

Rule argument

spec: <toplevel> name: sorted-lt-post seq: ⊦ m1 < m ∧ sorted(zbrar, n, m) → (zbrar[n].key < zbrar[n + m1].key ↔ 0 ≠ m1) subst: [m1, m, zbrar, n] → [m1, m, zbrar, n]

Additional information

Used terms: m1, m, zbrar, n