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Proof step 31 from proof prepost-resize (previous step)

(m0 < 0 ∨ 0 + m ≤ m0 ⊃ mkkeyarray(n0)[m0];kar[m0 + 0 - 0]) = key-index(key0, m2), kar[m1] = key-index(key, m2), 2exp-size(n0), 2exp-size(# kar), m1 < n0, m0 + 1 < n0, m1 + 1 < n0, m0 + 1 < minsize, m1 < minsize, m1 < # kar, m1 + 1 < minsize, m0 < m, m < minsize, m < n0, m1 < m, m0 < minsize, m0 < n0, m0 < # kar, m0 < # mkkeyarray(n0), heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), minsize ≤ n0, m ≤ # kar ⊦ m1 = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 32:
kar[m1] = key-index(key, m2), kar[m0] = key-index(key0, m2), 2exp-size(# kar), 2exp-size(n0), m0 < # kar, m0 < minsize, m1 < m, m < n0, m < minsize, m0 < m, m1 + 1 < minsize, m1 < # kar, m1 < minsize, m0 + 1 < minsize, m1 + 1 < n0, m0 + 1 < n0, m1 < n0, m0 < n0, heap-order(kar, m), no-dups-idx(kar, m), valid-idx(kar, ar, m), m ≤ # kar, minsize ≤ n0 ⊦ m1 = m0

Rule argument

Additional information

Used simplifier rules: ⊦ # mkkeyarray(n) = n; (s)% ⊦ m - 0 = m; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ ¬ m < 0; (s)