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Proof step 18 from proof bin-heap-inv-write-other-fields (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), 2exp-size(# kar), n < # lpt, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m3. m3 < m → kar[m3].idx < # lpt ∧ lpt[n, mklp(n0, n1, lpf1, m2)][kar[m3].idx].gcheapidx = m3 ⊦ ∀ m0. m0 < m → kar[m0].idx < # lpt ∧ lpt[kar[m0].idx].gcheapidx = m0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
lpt[n] = mklp(m0, m1, lpf0, m2), 2exp-size(# kar), m3 < m, n < # lpt, m3 < # kar, heap-order(kar, m), no-dups-idx(kar, m), m ≤ # kar, ∀ m3. m3 < m → kar[m3].idx < # lpt ∧ lpt[n, mklp(n0, n1, lpf1, m2)][kar[m3].idx].gcheapidx = m3 ⊦ kar[m3].idx < # lpt ∧ lpt[kar[m3].idx].gcheapidx = m3

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic