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Proof step 71 from proof refine-read (previous step)

# avol0 = # lpt + m6, # buf5 = n0 + n2 + n1, avol0[m6 + m8] = mapped(buf1), avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n1 ≤ # buf5, m7 + n1 ≤ LEB_SIZE, m6 ≤ # avol0, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ∃ buf1. # buf1 = # buf5 ∧ range=(buf5, 0, buf1, 0, n2) ∧ range=(buf5, n2 + n1, buf1, n2 + n1, n0)

User applied rule exists right

And closed the goal!

Rule argument

pos: right 1 terms: buf5 abort: F discard: T computed: F

Additional information

Used simplifier rules: ⊦ range=(buf, n, buf, n, m) ↔ n + m ≤ # buf; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m < n → n ≠ 0; (s)% ⊦ m + m0 < n → ¬ n + n0 < m; (s) Used terms: buf5