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Proof step 12 from proof abs-istore-reduce-write (previous step)

# lpt = # avol, lpt[n] = mklp(m4, m5, lpf0, m6), istore[n] = indexblock(indx0, lax0, m3), ∀ n. (n < # avol ∧ lpt[n].flags = LP_INDEX_NODES ↔ n ∈ istore) ∧ (n ∈ istore → abs-leb(avol[n], istore[n], lpt[n]) ∧ lpt[n].ref-size = istore[n].ref-size), ∀ n0. (n0 < # avol ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].flags = LP_INDEX_NODES ↔ n0 ∈ istore[n, indexblock(indx, lax, m)]) ∧ ( n0 ∈ istore[n, indexblock(indx, lax, m)] → abs-leb(avol[n, aleb][n0], istore[n, indexblock(indx, lax, m)][n0], lpt[n, mklp(m0, m1, lpf, m2)][n0]) ∧ lpt[n, mklp(m0, m1, lpf, m2)][n0].ref-size = istore[n, indexblock(indx, lax, m)][n0].ref-size) ⊦ n < # avol ∧ ((lpf0 = LP_INDEX_NODES → m4 = m3) → m0 = m ∧ lpf = LP_INDEX_NODES) ∧ ( (lpf0 = LP_INDEX_NODES → abs-leb(avol[n], indexblock(indx0, lax0, m3), mklp(m4, m5, LP_INDEX_NODES, m6))) → abs-leb(aleb, indexblock(indx, lax, m), mklp(m0, m1, lpf, m2)))

User applied rule all left

And closed the goal!

Rule argument

pos: left 5 terms: n abort: F discard: T computed: T

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ n ∈ istore[n, iblock]; (s)% ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ istore[n, iblock][n] = iblock; (s)% ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ indexblock(indx, lax, m).ref-size = m; (s) Used terms: n