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

lpt[n] = mklp(m0, m1, LP_FREE, m2), n < # lpt, m ≤ # lpt ⊦ gc-heap(lpt[n, lp], nx + n ', m) = gc-heap(lpt, nx, m)

User applied rule structural induction

And obtained the following new goals

Proof step 4:
lpt[n] = mklp(m0, m1, LP_FREE, m2), n < # lpt, m3 +1 ≤ # lpt, ∀ lpt, n, m0, m1, m2, lp, nx. lpt[n] = mklp(m0, m1, LP_FREE, m2) ∧ n < # lpt ∧ m3 ≤ # lpt → gc-heap(lpt[n, lp], nx + n ', m3) = gc-heap(lpt, nx, m3) ⊦ gc-heap(lpt[n, lp], nx + n ', m3 +1) = gc-heap(lpt, nx, m3 +1)

Rule argument

indvar: m

Additional information

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