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Proof step 77 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), avol1 = subarray(avol0, m6, # lpt), n3 ≠ 0, m8 < # lpt, n3 < n, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m6, # lpt)), is-aligned(n, EB_PAGE_SIZE), is-aligned(n0 + # buf0, EB_PAGE_SIZE), is-aligned(n3, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n2 + n3 ≤ # buf, n2 + n ≤ # buf, n0 + # buf0 + n ≤ LEB_SIZE, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨apersistence_io_write#(m8, n0 + # avol0[m6 + m8].data, n2, n, buf, adr, m1, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n0) + subarray(buf, n2, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n0) + subarray(buf, n2, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err1)

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 78:
# avol0 = # lpt + m6, avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol0[m6 + m8] = mapped(buf0), avol = avol1, avol1 = subarray(avol0, m6, # lpt), m = m7, m0 = n4 + # avol0[m6 + m8].data, m1 = m8, n0 = n, n1 = n2, ns = orphans, plog = log, avol0[m6 + m8].mapped?, m6 + m8 < # avol0, n3 < n, m8 < # lpt, disk-layout(mksb(adr, m7, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(n3, EB_PAGE_SIZE), is-aligned(n4 + # buf0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m7, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), n4 + # buf0 + n ≤ LEB_SIZE, n2 + n ≤ # buf, n2 + n3 ≤ # buf, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟨if m1 < # avol ∧ avol[m1].mapped? ∧ # avol[m1].data ≤ m0 ∧ is-aligned(m0, EB_PAGE_SIZE) ∧ is-aligned(n0, EB_PAGE_SIZE) ∧ m0 + n0 ≤ LEB_SIZE ∧ n1 + n0 ≤ # buf then {fail_or_success#(; ; err); if err = ESUCCESS then if n0 ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n0)) else choose n with n < n0 ∧ is-aligned(n, EB_PAGE_SIZE) in if n ≠ 0 then avol[m1] := mapped(avol[m1].data + mkempbuf(m0 - # avol[m1].data) + subarray(buf, n1, n)) ifnone skip} else abort⟩ ( avol = subarray(avol0, m6, # lpt)[m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))] ∧ is-encoded(log, avol0[m6 + m8, mapped(avol0[m6 + m8].data + mkempbuf(n4) + subarray(buf, n2, n3))][m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err), n3 = 0

Rule argument

pos: right 1

Additional information

Used simplifier rules: apersistence_io_write# (LNUM, OFFSET, N0, N, BUF, PROOTADR, PMAXINO, PLOG, PLPT, PORPHANS ; PVOL ; ERR ) {if LNUM < # PVOL ∧ PVOL[LNUM].mapped? ∧ # PVOL[LNUM].data ≤ OFFSET ∧ is-aligned(OFFSET, EB_PAGE_SIZE) ∧ is-aligned(N, EB_PAGE_SIZE) ∧ OFFSET + N ≤ LEB_SIZE ∧ N0 + N ≤ # BUF then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then if N ≠ 0 then PVOL[LNUM] := mapped ( PVOL[LNUM].data + mkempbuf(OFFSET - # PVOL[LNUM].data) + subarray(BUF, N0, N)) else choose N1 with N1 < N ∧ is-aligned(N1, EB_PAGE_SIZE) in if N1 ≠ 0 then PVOL[LNUM] := mapped ( PVOL[LNUM].data + mkempbuf(OFFSET - # PVOL[LNUM].data) + subarray(BUF, N0, N1)) ifnone skip} else abort };%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)% ⊦ aleb.mapped? ↔ aleb ≠ unmapped; (ss)% ⊦ unmapped ≠ mapped(buf); (s)