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Proof step 13 from proof inv-flashsize-app (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ ¬ n < # x → (x + y)[n] = y[n - # x]
Proof step 15:
# x0 = # lax0, # x1 = # lax1, (lax0 + lax1)[n] = @(m, m0), n < # x0, n < # lax0 + # lax1, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize ⊦ m0 = (x0 + x1)[n].flashsize
Proof step 17:
# x0 = # lax0, # x1 = # lax1, (lax0 + lax1)[n] = @(m, m0), n < # lax0 + # lax1, ∀ n. n < # lax1 → lax1[n].size = x1[n].flashsize, ∀ n. n < # lax0 → lax0[n].size = x0[n].flashsize ⊦ m0 = x1[n - # x0].flashsize, n < # x0

Rule argument

spec: list-del name: get-append-grt seq: ⊦ ¬ n < # x → (x + y)[n] = y[n - # x] subst: [n, y, x] → [n, x1, x0] flags: <all paths>

Additional information

Used terms: n, x1, x0