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Proof step 16 from proof gc-heap-update-h (previous step)

lpt[n] = mklp(m, m4, LP_GROUP_NODES, m5), n < # lpt ⊦ n ∈ nx, ∀ ki0. ki0 ∈ gc-heap(lpt, nx, n) ++ key-index(m6, n) ↔ ki0 = key-index(m6, n) ∨ ki0 ∈ gc-heap(lpt, nx, n) -- key-index(m, n)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 17:
lpt[n] = mklp(m, m4, LP_GROUP_NODES, m5), n < # lpt, key-index(m, n) ∈ gc-heap(lpt, nx, n) ⊦ # gc-heap(lpt, nx, n) = 0, gc-heap(lpt, nx, n) = ∅, key-index(m, n) = key-index(m6, n), n ∈ nx

Rule argument

Additional information

Used simplifier rules: size-zero-01: ⊦ gchs ≠ ∅ → # gchs ≠ 0; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%ne-01: ⊦ ki ∈ gchs → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]% ⊦ ki ∈ gchs ++ ki0 ↔ ki = ki0 ∨ ki ∈ gchs; (s)% ⊦ ki ∈ gchs -- ki0 ↔ ki ≠ ki0 ∧ ki ∈ gchs; (s)% ⊦ ki ≠ ki0 → (ki ∈ gchs ++ ki0 ↔ ki ∈ gchs); (s)