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Proof step 320 from proof refine-read-buf (previous step)

# buf2 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, LEB_SIZE = n0 + # buf4, LEB_SIZE = n1 + # buf1, avol0[n2] = mapped(buf), avol0[m2] = mapped(buf4), avol1[m2] = mapped(buf1), n2 < # avol1, m2 < # avol1, m4 < EB_PAGE_SIZE, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, # buf4 ≤ LEB_SIZE, n ≤ # buf3, # buf1 ≤ LEB_SIZE, rofs ∧ m2 = n2 → m6 = # buf ∧ avol1[n2] = mapped(buf + subarray(buf2, 0, m4)) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ avol1[n2] = mapped(buf) ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4), ¬ rofs ∧ m2 = n2 → avol1[n2] = mapped(buf + subarray(buf2, 0, m4)), rofs → m6 ≤ # buf, ¬ rofs → # buf = m6, m2 ≠ n2 → buf1 = buf4 ⊦ copy(buf4 + mkempbuf(n0), m0, buf3, 0, n) = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), m2 = n2 ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

User applied rule case distinction

And obtained the following new goals

Proof step 321:
# avol0 = # avol1, # lpt0 = # avol1, # buf2 = EB_PAGE_SIZE, LEB_SIZE = n1 + # buf1, LEB_SIZE = n0 + # buf4, avol1[m2] = mapped(buf1), avol0[m2] = mapped(buf4), avol0[n2] = mapped(buf), m2 = n2, m4 < EB_PAGE_SIZE, m2 < # avol1, n2 < # avol1, awbuf-inv(avol1, buffered(n2)), ebm-vol-inv(avol0), is-aligned(m6, EB_PAGE_SIZE), # buf1 ≤ LEB_SIZE, n ≤ # buf3, # buf4 ≤ LEB_SIZE, m0 + n ≤ LEB_SIZE, ¬ rofs → # buf = m6, rofs → m6 ≤ # buf, ¬ rofs ∧ m2 = n2 → avol1[n2] = mapped(buf + subarray(buf2, 0, m4)), rofs ∧ m2 = n2 → m6 = # buf ∧ avol1[n2] = mapped(buf + subarray(buf2, 0, m4)) ∨ m6 < # buf ∧ m6 + m4 < # buf ∧ avol1[n2] = mapped(buf) ∧ subarray(buf2, 0, m4) = subarray(buf, m6, m4) ⊦ copy(buf4 + mkempbuf(n0), m0, buf3, 0, n) = copy(buf1 + mkempbuf(n1), m0, buf3, 0, n), m2 = n2 ∧ m0 ≤ m6 + m4 ∧ m6 ≤ m0 + n

Rule argument

pos: left 23

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic