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Proof step 266 from proof refine-read-buf (previous step)

# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, # buf + n4 + n2 = # buf3, n1 + n5 = n4 + n2, LEB_SIZE = n3 + n2 + # buf0 + # buf, avol0[m2] = mapped(buf0 + buf), avol1[m2] = mapped((buf0 + buf) + subarray(buf2, 0, n2)), n0 < n4, m2 < # avol1, n2 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), # buf0 ≤ LEB_SIZE, n1 ≤ n2 + n3, # buf ≤ # buf3, n2 ≤ n1 ⊦ (n2 + n0 < n1 ⊃ empty;subarray(buf3, n1 + # buf, n5)[n2 + n0 - n1]) = (n0 + n2 < n1 ⊃ (subarray(buf2, 0, n2) + mkempbuf(n3))[n0 + n2];subarray(buf3, n1 + # buf, n5)[n0 + n2 - n1])

User applied rule case distinction

And obtained the following new goals

Proof step 267:
# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, n1 + n5 = n4 + n2, # buf + n4 + n2 = # buf3, LEB_SIZE = n3 + n2 + # buf0 + # buf, avol1[m2] = mapped((buf0 + buf) + subarray(buf2, 0, n2)), avol0[m2] = mapped(buf0 + buf), n2 < EB_PAGE_SIZE, m2 < # avol1, n0 < n4, n2 + n0 < n1, awbuf-inv(avol1, buffered(m2)), ebm-vol-inv(avol0), is-aligned(# buf0 + # buf, EB_PAGE_SIZE), n2 ≤ n1, # buf ≤ # buf3, n1 ≤ n2 + n3, # buf0 ≤ LEB_SIZE ⊦ empty = (n0 + n2 < n1 ⊃ (subarray(buf2, 0, n2) + mkempbuf(n3))[n0 + n2];subarray(buf3, n1 + # buf, n5)[n0 + n2 - n1])

Rule argument

pos: right 1

Additional information

Used simplifier rules: ⊦ m < n ↔ ¬ n ≤ m; (ss)%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ n → (n < m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]