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

lpt[n1] = mklp(m, m0, lpf, m1), n ≤ # lpt ⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx, n) ↔ n1 < n ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES

User applied rule structural induction

And obtained the following new goals

Proof step 5:
lpt[n1] = mklp(m, m0, lpf, m1), n2 +1 ≤ # lpt, ∀ lpt, n1, m, m0, lpf, m1, n0, nx. lpt[n1] = mklp(m, m0, lpf, m1) ∧ n2 ≤ # lpt → (key-index(n0, n1) ∈ gc-heap(lpt, nx, n2) ↔ n1 < n2 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES) ⊦ key-index(n0, n1) ∈ gc-heap(lpt, nx, n2 +1) ↔ n1 < n2 +1 ∧ ¬ n1 ∈ nx ∧ m = n0 ∧ lpf = LP_GROUP_NODES

Rule argument

indvar: n

Additional information

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