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Proof step 12 from proof gc-heap-update-log-h (previous step)

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

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
lpt[m3] = mklp(m, m4, LP_GROUP_NODES, m5), lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), n < # lpt, m3 < # lpt, n ∈ nx, n ≤ m3, n < m3 → 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) ++ key-index(m, m3) = gc-heap(lpt, nx, m3) ++ key-index(m, m3), m3 ∈ nx

Rule argument

Additional information

Used simplifier rules: unc: ⊦ gchs ∪ gchs0 = gchs0 ∪ gchs; from specification set-union[gc-heap-rename-gc-heap-base-keyindex-set]%una: ⊦ (gchs ∪ gchs0) ∪ gchs1 = gchs ∪ gchs0 ∪ gchs1; from specification set-union[gc-heap-rename-gc-heap-base-keyindex-set]% ⊦ gchs ∪ ∅ = gchs; (s)% ⊦ (gchs ++ ki) ∪ gchs0 = (gchs ∪ gchs0) ++ ki; (s)