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Proof step 18 from proof inv-flashsize-app (previous step)

# x0 = # lax0, # x1 = # lax1, (lax0 + lax1)[n] = @(m, m0), n < # lax0 + # lax1, # lax0 ≤ n, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize ⊦ lax1 = [], m0 = x1[n - # lax0].flashsize

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 19:
# x1 = # lax1, # x0 = # lax0, (lax0 + lax1)[n] = @(m, m0), n = n0 + # lax0, n < # lax0 + # lax1, # lax0 ≤ n, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize ⊦ lax1 = [], m0 = x1[n0].flashsize

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [m, n, n0] → [n, # lax0, n0]

Additional information

Used simplifier rules: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: n, # lax0, n0