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Proof step 8 from proof gc-heap-write-above (previous step)

lpt[m0] = mklp(m, m1, lpf, m2), m0 < # lpt, m0 < n, n < # lpt, m0 + 1 < # lpt, m0 < # lpt[n, lp], ∀ lpt, n, lp, nx. m0 < # lpt ∧ n < # lpt ∧ m0 ≤ n → gc-heap(lpt[n, lp], nx, m0) = gc-heap(lpt, nx, m0) ⊦ gc-heap(lpt[n, lp], nx, m0) ∪ (¬ m0 ∈ nx ∧ lpt[n, lp][m0].flags = LP_GROUP_NODES ⊃ {key-index(lpt[n, lp][m0].ref-size, m0)} ;∅) = gc-heap(lpt, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 9:
lpt[m0] = mklp(m, m1, lpf, m2), m0 < # lpt, m0 < n, n < # lpt, m0 + 1 < # lpt, ∀ lpt, n, lp, nx. m0 < # lpt ∧ n < # lpt ∧ m0 ≤ n → gc-heap(lpt[n, lp], nx, m0) = gc-heap(lpt, nx, m0) ⊦ gc-heap(lpt[n, lp], nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅) = gc-heap(lpt, nx, m0) ∪ (¬ m0 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m0);∅)

Rule argument

Additional information

Used simplifier rules: ⊦ mklp(n2, n3, lpf, m).ref-size = n2; (s)% ⊦ mklp(n2, n3, lpf, m).flags = lpf; (s)% ⊦ # lpt[n, lp] = # lpt; (s)% ⊦ {ki} = ∅ ++ ki; (s)% ⊦ n < m → lpt[m, lp][n] = lpt[n]; (s)