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Proof step 3 from proof gc-heap-write-above (previous step)

m < # lpt, n < # lpt, m ≤ n ⊦ gc-heap(lpt[n, lp], nx, m) = gc-heap(lpt, nx, m)

User applied rule structural induction

And obtained the following new goals

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