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Proof step 9 from proof gc-heap-update-log-h (previous step)

lpt[m3] = mklp(m, m4, lpf, m5), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt, m3 < # lpt, n ∈ nx, n ≤ m3, ∀ lpt, n, n0, n1, n2, nx, m0, m1, m2. lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ n < m3 ∧ n < # lpt ∧ n ∈ nx ∧ m3 ≤ # lpt → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅)

User applied rule all left

And obtained the following new goals

Proof step 10:
lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[m3] = mklp(m, m4, lpf, m5), m3 < # lpt, n < # lpt, n ∈ nx, n ≤ m3, lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2) ∧ n < m3 ∧ n < # lpt ∧ n ∈ nx ∧ m3 ≤ # lpt → gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅)

Rule argument

pos: left 7 terms: lpt, n, n0, n1, n2, nx, m0, m1, m2 abort: F discard: T computed: F

Additional information

Used terms: lpt, n, n0, n1, n2, nx, m0, m1, m2