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Proof step 10 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf3), avol[m5] = mapped(buf1), buf = mkbuf(m2 * ENCODED_NAT_SIZE), buf0 = buf, m = 0, m0 = m1, n = m2 * ENCODED_NAT_SIZE, n0 = 0, avol[m0].mapped?, m0 < # 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, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), n0 + n ≤ # buf0, m + n ≤ LEB_SIZE, m0 < # avol → m0 < # avol, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m0].data + mkempbuf(LEB_SIZE - # avol[m0].data), m, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf0, 0, buf, 0, n0) ∧ range=(buf0, n0 + n, buf, n0 + n, # buf0 - n0 + n) in buf0 := buf; if err = ESUCCESS then persistence_io_decode_orphans#(m2, buf0; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 11:
m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf3), avol[m5] = mapped(buf1), 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, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪fail_or_success#(; ; err); buf3 := mkbuf(m2 * ENCODED_NAT_SIZE); if err = ESUCCESS then buf3 := copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), 0, buf3, 0, m2 * ENCODED_NAT_SIZE) else {n0 := 0; n := m2 * ENCODED_NAT_SIZE; choose buf1 with # buf1 = # buf3 ∧ range=(buf3, 0, buf1, 0, n0) ∧ range=(buf3, n0 + n, buf1, n0 + n, # buf3 - n0 + n) in buf3 := buf1}; if err = ESUCCESS then persistence_io_decode_orphans#(m2, buf3; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Rule argument

Additional information

Used simplifier rules: # avol = sb.main + mainareasize ⊦ disk-layout(sb, mainareasize) → # avol ≠ 0; (s)% ⊦ mksb(adr, m, m0, m1, m2, m3, m4).main = m4; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)