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Proof step 13 from proof prepost-get-min (previous step)

kar[0] = key-index(key0, m0), 2exp-size(# kar), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar ⊦ # kar = 0, # keyset(kar, m) = 0, keyset(kar, m) = ∅, key-index(key0, m0) ∈ keyset(kar, m) ∧ (ki ∈ keyset(kar, m) → ¬ ki.key < key0)

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: key-index name: elim seq: ⊦ key = ki.key ∧ m = ki.idx ↔ ki = key-index(key, m) subst: [ki, key, m] → [ki, key, m1]

Additional information

Used simplifier rules: ⊦ key = ki.key ∧ m = ki.idx ↔ ki = key-index(key, m); (elim) Used terms: ki, key, m1