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Proof step 34 from proof replay-lpt-at (previous step)

lpt[n0] = mklp(0, m4, lpf0, m5), lpt[m] = mklp(m0, m1, lpf, m2), n0 < # lpt, m < # lpt, m ≤ n0, lpf = LP_FREE ∨ m ∈ nx ⊦ replay-lpt(lpt, nx, n0)[n0, mklp(0, 0, LP_FREE, m5)][m] = replay-lpt(lpt, nx, n0)[m], lpf0 = LP_FREE, n0 ∈ nx

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 35:
⊦ m ≠ n → lpt[n, lp][m] = lpt[m]

Rule argument

spec: array, inst: gc-heap-base-index-array-base name: Put-other seq: ⊦ m ≠ n → lpt[n, lp][m] = lpt[m] subst: [m, lp, n, lpt] → [m, mklp(0, 0, LP_FREE, m5), n0, replay-lpt(lpt, nx, n0)] flags: <all paths>

Additional information

Used simplifier rules: replay-lpt-size: n ≤ # lpt ⊦ # replay-lpt(lpt, nx, n) = # lpt;%replay-lpt-at-above: n ≤ m, m < # lpt ⊦ replay-lpt(lpt, nx, n)[m] = lpt[m];% ⊦ m < n → m ≤ n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # lpt ⊦ lpt[m, lp][m] = lp; (s)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s)% ⊦ m ≤ m; (s)%⊦ mklp(m, m0, lpf, m1) = mklp(m2, m3, lpf0, m4) ↔ m = m2 ∧ m0 = m3 ∧ lpf = lpf0 ∧ m1 = m4; (ws) Used terms: m, mklp(0, 0, LP_FREE, m5), n0, replay-lpt(lpt, nx, n0)