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Proof step 8 from proof inv-write (previous step)

m6 + # lpt = # avol, avol[m6 + m8] = mapped(buf0), avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), m8 < # lpt, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-aligned(n, EB_PAGE_SIZE), is-aligned(m7, EB_PAGE_SIZE), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), n0 + n ≤ # buf, # buf0 ≤ m7, m7 + n ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪ebm_avol_write#(m6 + m8, m7, n0, n, buf; avol; err)⟫ ( (∃ lpt0, log, orphans. disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0) ∧ m6 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[0].data) ∧ avol[m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ avol[m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m2].data = logoff) ∧ is-encoded(log, avol[m2].data) ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

User applied rule insert program lemma

And obtained the following new goals

Proof step 9:
ebm-vol-inv(avol), m < # avol, avol[m].mapped?, # avol[m].data ≤ m0, is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ ⟪ebm_avol_write#(m, m0, n0, n, buf; avol; err)⟫ ebm-vol-inv(avol)
Proof step 10:
m6 + # lpt = # avol, avol[0] = mapped(buf1), avol[m3] = mapped(buf2), avol[m2] = mapped(buf3), avol[m6 + m8] = mapped(buf0), buf4 = buf, m10 = m7, m9 = m6 + m8, n1 = n, n2 = n0, avol[m6 + m8].mapped?, m8 < # lpt, m6 + m8 < # avol, disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt), ebm-vol-inv(avol), is-aligned(m7, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), buf1), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), # buf0 ≤ m7, # avol[m6 + m8].data ≤ m7, m7 + n ≤ LEB_SIZE, n0 + n ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ [ebm_avol_write#(m6 + m8, m7, n0, n, buf; avol; err)] ( ebm-vol-inv(avol) → (∃ lpt0, log, orphans. disk-layout(mksb(adr, m1, m2, m3, m4, m5, m6), # lpt0) ∧ m6 + # lpt0 = # avol ∧ avol[0].mapped? ∧ is-encoded(mksb(adr, m1, m2, m3, m4, m5, m6), avol[0].data) ∧ avol[m3].mapped? ∧ is-encoded-pad(orphans, m4, avol[m3].data) ∧ avol[m2].mapped? ∧ (logoff ≠ LEB_SIZE → # avol[m2].data = logoff) ∧ is-encoded(log, avol[m2].data) ∧ mapped-full?(avol, m5, lptlebs(# lpt0, LEB_SIZE)) ∧ is-encoded(lpt0, lebs(avol, m5, lptlebs(# lpt0, LEB_SIZE)))) ∧ ebm-vol-inv(avol))

Rule argument

spec: ebm-avol-asm name: inv-write seq: ebm-vol-inv(avol), m < # avol, avol[m].mapped?, # avol[m].data ≤ m0, is-aligned(m0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), m0 + n ≤ LEB_SIZE, n0 + n ≤ # buf ⊦ ⟪ebm_avol_write#(m, m0, n0, n, buf; avol; err)⟫ ebm-vol-inv(avol) subst: [buf, n, n0, m0, m, avol, err] → [buf, n, n0, m7, m6 + m8, avol, err] flags: <all paths>

Additional information

Used simplifier rules: 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)% ⊦ mapped(buf).mapped?; (s)% ⊦ mapped(buf).data = buf; (s)