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Proof step 3 from proof gc-heap-fill-free-h (previous step)

m ≤ n ⊦ # gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m) = 0, gc-heap(fill(mklparray(n), mklp(n0, n1, LP_FREE, n2)), nx, m) = ∅

User applied rule structural induction

And obtained the following new goals

Proof step 4:
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) = ∅

Rule argument

indvar: m

Additional information

Used simplifier rules: gc-heap-base: ⊦ gc-heap(lpt, nx, 0) = ∅;%nat freely generated by 0, +1;;