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Proof step 14 from proof abs-istore-set-refsize (previous step)

n5 < # lpt ∧ lpf0 = LP_INDEX_NODES ↔ n5 ∈ istore, lpt[n5] = mklp(m5, m6, lpf0, m7), istore[n, indexblock(indx, lax, m0)][n5] = indexblock(indx0, lax0, m), lpt[n] = mklp(n0, n1, LP_INDEX_NODES, n4), istore[n] = indexblock(indx, lax, n3), lpt[n, mklp(m0, n1, LP_INDEX_NODES, n2)][n5] = mklp(m1, m2, lpf, m3), istore[n5] = indexblock(indx1, lax1, m4), n5 = n, n ∈ istore, n5 ∈ istore → abs-leb(avol[n5], indexblock(indx1, lax1, m4), mklp(m4, m6, lpf0, m7)) ∧ m5 = m4 ⊦ (n5 < # lpt ∧ lpf = LP_INDEX_NODES ↔ n5 ∈ istore[n, indexblock(indx, lax, m0)]) ∧ (n5 ∈ istore[n, indexblock(indx, lax, m0)] → abs-leb(avol[n5], indexblock(indx0, lax0, m), mklp(m, m2, lpf, m3)) ∧ m1 = m)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 15:
istore[n] = indexblock(indx1, lax1, n0), lpt[n] = mklp(n0, m2, LP_INDEX_NODES, n4), n < # lpt, abs-leb(avol[n], indexblock(indx1, lax1, n0), mklp(n0, m2, LP_INDEX_NODES, n4)), n ∈ istore ⊦ abs-leb(avol[n], indexblock(indx1, lax1, m1), mklp(m1, m2, LP_INDEX_NODES, m3))

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ n ∈ istore[n, iblock]; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)%⊦ indexblock(indx, lax, m) = indexblock(indx0, lax0, m0) ↔ indx = indx0 ∧ lax = lax0 ∧ m = m0; (ws)% ⊦ istore[n, iblock][n] = iblock; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)