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

# buf1 = EB_PAGE_SIZE, # lpt0 = # avol1, # avol0 = # avol1, avol0[m4] = mapped(buf2), # avol1[m4].data < # buf2 + m2, LEB_SIZE < # buf2 + m2 + n, m2 < EB_PAGE_SIZE, m4 < # avol1, awbuf-inv(avol1, buffered(m4)), ebm-vol-inv(avol0), is-aligned(# buf2, EB_PAGE_SIZE), n ≤ # buf, # avol1[m4].data + n ≤ LEB_SIZE, ∀ n0. n0 < # avol1 → (n0 ≠ m4 → avol1[n0] = avol0[n0]) ∧ (n0 = m4 → avol1[m4] = mapped(buf2 + subarray(buf1, 0, m2))) ⊦

User applied rule all left

And closed the goal!

Rule argument

pos: left 14 terms: m4 abort: F discard: F computed: T

Additional information

Used simplifier rules: fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).data = buf; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # subarray(buf, m, n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n < m + n0 ↔ n < n0; (s)% ⊦ ¬ n < n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ m < n → (n ≤ m ↔ false); (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf: ⊦ m < n ∧ n < n0 → m +1 < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%transitivity: ⊦ n < n0 ∧ n0 < n1 → n < n1; (forward) from specification oelem[nat-set]% ⊦ m < n → n ≠ 0; (s)% ⊦ m +1 = m + 1; (s)% ⊦ m < n → ¬ n < m; (s) Used terms: m4