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Proof step 12 from proof gc-heap-write-other-h (previous step)

lpt[n] = mklp(m0, m1, lpf0, m2), lpt[m3] = mklp(m, m4, lpf, m5), lpt[n, mklp(n0, n1, lpf1, n2)][m3] = mklp(m6, m7, lpf2, m8), gc-heap(lpt[n, mklp(n0, n1, lpf1, n2)], nx, m3) = gc-heap(lpt, nx, m3), m3 < # lpt, n < # lpt ⊦ lpf0 = LP_GROUP_NODES, lpf1 = LP_GROUP_NODES, gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf2 = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅) = gc-heap(lpt, nx, m3) ∪ (¬ m3 ∈ nx ∧ lpf = LP_GROUP_NODES ⊃ ∅ ++ key-index(m, m3);∅)

Heuristic weak cut applied rule cut formula

And closed the goal!

Rule argument

fma: m3 = n

Additional information

Used simplifier rules: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m]; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws)% ⊦ m < # lpt → lpt[m, lp][m] = lp; (s)% ⊦ 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) Used formulas: m3 = n