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Proof step 22 from proof gc-heap-remove-wbufs-h (previous step)

(n0 ∈ ns ⊃ mklp(m, LEB_SIZE, lpf, m1);mklp(m, m0, lpf, m1)) = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), nx, n0) = gc-heap(lpt, nx, n0), n0 < # lpt, n0 ∈ nx ∨ lpf0 ≠ LP_GROUP_NODES ⊦ gc-heap(lpt, nx, n0) ∪ ∅ = gc-heap(lpt, nx, n0) ∪ (¬ n0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 23:
(n0 ∈ ns ⊃ mklp(m, LEB_SIZE, lpf, m1);mklp(m, m0, lpf, m1)) = mklp(m2, m3, lpf0, m4), lpt[n0] = mklp(m, m0, lpf, m1), gc-heap(lpt.mapIndices(ns, λ lp. lp.size:= LEB_SIZE), nx, n0) = gc-heap(lpt, nx, n0), n0 < # lpt ⊦ lpf0 = LP_GROUP_NODES, n0 ∈ nx, (lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, n0);∅) ⊆ gc-heap(lpt, nx, n0)

Rule argument

Additional information

Used simplifier rules: ⊦ ∅ ⊆ gchs; (s)% ⊦ gchs ∪ gchs0 = gchs0 ↔ gchs ⊆ gchs0; (s)%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)