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Proof step 25 from proof binheap-inv-remove-wbufs (previous step)

(m4 ∈ ns ∧ m4 < # lpt ⊃ lpt[m4].size:= LEB_SIZE;lpt[m4]) = mklp(m1, m2, lpf, m3), lpt[m4] = mklp(m0, m5, lpf0, m6), kar[m6] = key-index(natkey, m4), 2exp-size(# kar), m4 < # lpt, m6 < m, m6 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = m6

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
(m4 ∈ ns ⊃ mklp(m0, LEB_SIZE, lpf0, m6);mklp(m0, m5, lpf0, m6)) = mklp(m1, m2, lpf, m3), lpt[m4] = mklp(m0, m5, lpf0, m6), kar[m6] = key-index(natkey, m4), 2exp-size(# kar), m6 < # kar, m4 < # lpt, m6 < m, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar ⊦ m3 = m6

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(m, m0, lpf, m1).size:= m3 = mklp(m, m3, lpf, m1); (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat