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Proof step 120 from proof refine-read-buf (previous step)

# buf3 = n4 + n2, # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, (n0 + # buf4) + n3 + n2 = LEB_SIZE, n1 + n5 = n4 + n2, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), m2 < # avol1, n2 + n0 < EB_PAGE_SIZE, n0 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), n1 ≤ n2 + n3, # buf4 ≤ LEB_SIZE, n2 ≤ n1 ⊦ EB_PAGE_SIZE = 1, n0 = 0, #(subarray(buf2, n0, n2) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), n2, n4)) = #(subarray(subarray(buf2, 0, n2 + n0) + mkempbuf(n3), n0, n1) + subarray(buf3, n1, n5)) ∧ (∀ n. n < #(subarray(buf2, n0, n2) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), n2, n4)) → (subarray(buf2, n0, n2) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), n2, n4))[n] = (subarray(subarray(buf2, 0, n2 + n0) + mkempbuf(n3), n0, n1) + subarray(buf3, n1, n5))[n])

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 121:
# buf3 = n4 + n2, # avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, (n0 + # buf4) + n3 + n2 = LEB_SIZE, n1 + n5 = n4 + n2, avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf4 + subarray(buf2, 0, n2 + n0)), n < n4 + n2, n < n2 + n4, m2 < # avol1, n2 + n0 < EB_PAGE_SIZE, n0 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf4, EB_PAGE_SIZE), n1 ≤ n2 + n3, # buf4 ≤ LEB_SIZE, n2 ≤ n1 ⊦ EB_PAGE_SIZE = 1, (subarray(buf2, n0, n2) + subarray(mkempbuf(n1) + subarray(buf3, n1, n5), n2, n4))[n] = (subarray(subarray(buf2, 0, n2 + n0) + mkempbuf(n3), n0, n1) + subarray(buf3, n1, n5))[n], n0 = 0

Rule argument

Additional information

Used simplifier rules: ⊦ m < n → n ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)