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Proof step 5 from proof key-set-in (previous step)

2exp-size(# kar), heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar, m0), m0 ≤ # kar ⊦ ki ∈ keyset(kar, m0) ↔ (∃ m. m < m0 ∧ ki = kar[m])

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: bin-min-heap-inv name: key-set-extract-index seq: n ≤ # kar ⊦ ki ∈ keyset(kar, n) ↔ (∃ m. m < n ∧ ki = kar[m]) subst: [n, kar, ki] → [m0, kar, ki] flags: <all paths>

Additional information

Used terms: m0, kar, ki