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Proof step 16 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf), avol[0] = mapped(buf2), buf3 = mkbuf(m2 * ENCODED_NAT_SIZE), err = ESUCCESS, err = err0, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded-pad(orphans0, m2, buf), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪buf3 := copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), 0, buf3, 0, m2 * ENCODED_NAT_SIZE); if err = ESUCCESS then persistence_io_decode_orphans#(m2, buf3; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 17:
m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf), avol[m5] = mapped(buf1), buf3 = mkbuf(m2 * ENCODED_NAT_SIZE), err = err0, err = ESUCCESS, avol[m1].mapped?, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m2, buf), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), 0 + m2 * ENCODED_NAT_SIZE ≤ #(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data)), 0 + m2 * ENCODED_NAT_SIZE ≤ # buf3, m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, LEB_SIZE ≥ # avol[m1].data, logoff ≠ LEB_SIZE → # buf1 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪if err = ESUCCESS then persistence_io_decode_orphans# (m2, copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), 0, buf3, 0, m2 * ENCODED_NAT_SIZE); ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ ⌊ESUCCESS⌋ ; (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% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ # mkempbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ m; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m0 * m = 0 ↔ m0 = 0 ∨ m = 0; (ws)% ⊦ ENCODED_NAT_SIZE ≠ 0; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult% ⊦ ¬ n + (m - n) < m; (s)%⊦ n < # avol ∧ avol[n] = mapped(buf) ∧ ebm-vol-inv(avol) → ¬ LEB_SIZE < # buf; (s)