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Proof step 131 from proof refine-write (previous step)

# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[0] = mapped(buf1), avol0[m3] = mapped(buf2), avol0[m2] = mapped(buf3), avol = avol1, avol1 = subarray(avol0, m6, # lpt), m = m9, m0 = m7, m1 = m8, n0 = n, n1 = n2, ns = orphans, plog = log, avol[m1].mapped?, m1 < # avol, m8 < # lpt, disk-layout(mksb(adr, m9, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(subarray(avol0, m6, # lpt)), ebm-vol-inv(avol0), is-aligned(m0, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(mksb(adr, m9, 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)), # avol[m1].data ≤ m0, m0 + n0 ≤ LEB_SIZE, n1 + n0 ≤ # buf, m7 + n ≤ LEB_SIZE, # buf0 ≤ m7, n2 + n ≤ # buf, ⌊err0⌋ , m1 < # avol → m1 < # avol ∧ (avol[m1].mapped? → avol[m1].mapped? ∧ m1 < # avol), logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n0. ¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE) ⊦ ⟨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⟩ (avol = subarray(avol0, m6, # lpt) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 132:
# avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf0), avol0[m2] = mapped(buf3), avol0[m3] = mapped(buf2), avol0[0] = mapped(buf1), m8 < # lpt, disk-layout(mksb(adr, m9, 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(m7, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m9, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), # buf0 ≤ m7, n2 + n ≤ # buf, m7 + n ≤ LEB_SIZE, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf3 = logoff, ∀ n0. ¬ n0 < n ∨ ¬ is-aligned(n0, EB_PAGE_SIZE) ⊦ ⟨fail_or_success#(; ; err); avol := subarray(avol0, m6, # lpt); if err = ESUCCESS then if n ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(m7 - # avol[m8].data) + subarray(buf, n2, n)) else choose n1 with n1 < n ∧ is-aligned(n1, EB_PAGE_SIZE) in if n1 ≠ 0 then avol[m8] := mapped(avol[m8].data + mkempbuf(m7 - # avol[m8].data) + subarray(buf, n2, n1)) ifnone skip⟩ (avol = subarray(avol0, m6, # lpt) ∧ is-encoded(log, avol0[m2].data) ∧ is-encoded-pad(orphans, m4, avol0[m3].data) ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ # subarray(avol, m, n) = n; (s)% ⊦ n0 < n → subarray(avol, m, n)[n0] = avol[m + n0]; (s)