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Proof step 25 from proof gc-heap-update-h (previous step)

lpt[n] = mklp(n0, n1, LP_GROUP_NODES, n2), lpt[m3] = mklp(m, m4, LP_GROUP_NODES, m5), gc-heap(lpt[n, mklp(m0, m1, LP_GROUP_NODES, m2)], nx, m3) = (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ++ key-index(m0, n), n + 1 < # lpt, m3 < # lpt, n < # lpt, n < m3 ⊦ ki = key-index(m, m3) ∨ ki ≠ key-index(n0, n) ∧ ki ∈ gc-heap(lpt, nx, m3) ↔ ki ∈ (gc-heap(lpt, nx, m3) -- key-index(n0, n)) ∪ ((∅ ++ key-index(m, m3)) -- key-index(n0, n)), ki = key-index(m0, n), m3 = n, m3 ∈ nx, n ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 26:
⊦ ki ∈ gchs ∪ gchs0 ↔ ki ∈ gchs ∨ ki ∈ gchs0

Rule argument

spec: set-union, inst: gc-heap-rename-gc-heap-base-keyindex-set name: Union seq: ⊦ ki ∈ gchs ∪ gchs0 ↔ ki ∈ gchs ∨ ki ∈ gchs0 subst: [gchs0, gchs, ki] → [(∅ ++ key-index(m, m3)) -- key-index(n0, n), gc-heap(lpt, nx, m3) -- key-index(n0, n), ki] flags: <all paths>

Additional information

Used simplifier rules: ⊦ ki ∈ gchs -- ki0 ↔ ki ≠ ki0 ∧ ki ∈ gchs; (s)% ⊦ ki ∈ ∅ ++ ki0 ↔ ki = ki0; (s)%⊦ key-index(natkey, m) = key-index(natkey0, m0) ↔ natkey = natkey0 ∧ m = m0; (ws) Used terms: (∅ ++ key-index(m, m3)) -- key-index(n0, n), gc-heap(lpt, nx, m3) -- key-index(n0, n), ki