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Proof step 4 from proof gc-heap-fill-free-h (previous step)

m0 +1 ≤ n, ∀ n, n0, n1, n2, nx. m0 ≤ n → # gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0) = 0 ∨ gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0) = ∅ ⊦ # gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0 +1) = 0, gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0 +1) = ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
m0 < n, ∀ n, n0, n1, n2, nx. m0 ≤ n → # gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0) = 0 ∨ gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0) = ∅ ⊦ # gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0 + 1) = 0, gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m0 + 1) = ∅

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%size-zero-01: ⊦ gchs ≠ ∅ → # gchs ≠ 0; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%size-zero: ⊦ # gchs ≠ 0 → gchs ≠ ∅; (forward) from specification set-basic[gc-heap-rename-gc-heap-base-keyindex-set]%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m +1 = m + 1; (s)