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Proof step 11 from proof gc-heap-allocate-h (previous step)

lpt[m3] = mklp(m, m4, lpf, m5), lpt[n] = mklp(m0, m1, LP_FREE, m2), gc-heap(lpt[n, lp], nx + n ', m3) = gc-heap(lpt, nx, m3), n < # lpt, m3 < # lpt ⊦ gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ m3 ≠ n ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅)

Heuristic if-then-else split applied rule case distinction

And closed the goal!

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ gchs ∪ ∅ = gchs; (s)%una: ⊦ (gchs ∪ gchs0) ∪ gchs1 = gchs ∪ gchs0 ∪ gchs1; from specification set-union[gc-heap-rename-gc-heap-base-keyindex-set]%unc: ⊦ gchs ∪ gchs0 = gchs0 ∪ gchs; from specification set-union[gc-heap-rename-gc-heap-base-keyindex-set]% ⊦ gchs ∪ gchs0 = gchs0 ↔ gchs ⊆ gchs0; (s)% ⊦ ∅ ⊆ gchs; (s)% ⊦ ∅ ++ ki ⊆ gchs ↔ ki ∈ gchs; (s)%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ LP_FREE ≠ LP_GROUP_NODES; (s)% ⊦ (gchs ++ ki) ∪ gchs0 = (gchs ∪ gchs0) ++ ki; (s)