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Proof step 25 from proof prepost-remove (previous step)

ar1[m] = elemindex(a, m1), kar[m1] = key-index(key, m), ar = ar1[kar[m0 - 1].idx, ar1[kar[m0 - 1].idx].idx:= m1], bh = bin-heap(kar[m1, kar[m0 - 1]], m0 - 1), # keyset(kar, m0) ≠ 0, # kar ≠ 1, m0 - 1 ≠ m1, keyset(kar, m0) ≠ ∅, m0 ≠ 1, m1 ≠ 0, 2exp-size(# kar), (m1 - 1) / 2 < # kar, kar[m0 - 1].key < kar[m1, kar[m0 - 1]][(m1 - 1) / 2].key, kar[m0 - 1].idx < # ar1, m1 < m0, m1 < # kar, heap-order(kar, m0), no-dups-idx(kar, m0), valid-idx(kar, ar1, m0), key-index(key, m) ∈ keyset(kar, m0), 1 ≤ m1, m0 ≤ # kar ⊦ ⟪bin_min_heap_bubble_up#(m1; bh, ar)⟫ ( bh.size ≤ # bh.ar ∧ no-dups-idx(bh.ar, bh.size) ∧ valid-idx(bh.ar, ar, bh.size) ∧ 2exp-size(# bh.ar) ∧ heap-order(bh.ar, bh.size) ∧ id-idx(ar1, ar) ∧ keyset(bh.ar, bh.size) = keyset(kar, m0) -- key-index(key, m))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [m1, m2]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: m1, m2