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Proof step 17 from proof refine-commit (previous step)

# lpt2 = # lpt0, # lpt = # lpt0, # avol0 = # lpt0 + m10, # avol2 = # avol0, # avol0 = n0 + m10, avol2[m6] = mapped(buf4), avol2[m7] = mapped(buf3), avol2[0] = mapped(buf2), avol0[0] = mapped(buf), avol0[m2] = mapped(buf0), avol0[m1] = mapped(buf1), subarray(avol2, m10, n0) = subarray(avol0, m10, n0), disk-layout(mksb(adr, m, m6, m7, m8, m9, m10), # lpt0), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m10), # lpt0), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m10, # lpt0)), ebm-vol-inv(avol2), is-encoded(mksb(adr, m, m6, m7, m8, m9, m10), buf2), is-encoded(plog, buf1), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m10), buf), is-encoded(lpt0, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans1, m8, buf3), is-encoded-pad(ns, m4, buf0), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol2, m9, lptlebs(# lpt0, LEB_SIZE)), m10 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, err ≠ ESUCCESS → mksb(adr, m, m6, m7, m8, m9, m10) = mksb(adr0, m0, m1, m2, m4, m5, m10) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(n0, LEB_SIZE)) = lebs(avol0, m5, lptlebs(n0, LEB_SIZE)), err = ESUCCESS → adr = adr1 ∧ m = m3 ∧ buf4 = mkbuf(0) ∧ is-encoded(lpt, lebs(avol2, m9, lptlebs(n0, LEB_SIZE))) ∧ orphans1 = ns0, logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_commit#(lpt, adr1, m3, subarray(avol0, m10, # lpt0); ns0, adr0, m0, plog, lpt2, ns; err0)⟩ ( m0 = m ∧ adr0 = adr ∧ subarray(avol0, m10, # lpt0) = subarray(avol2, m10, n0) ∧ log = plog ∧ is-encoded(lpt2, lebs(avol2, m9, lptlebs(n0, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = ns0 ∧ err = err0)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 18:
# lpt = # lpt0, # lpt2 = # lpt0, # avol0 = # avol2, # avol2 = # lpt0 + m10, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol2[0] = mapped(buf2), avol2[m7] = mapped(buf3), avol2[m6] = mapped(buf4), subarray(avol2, m10, # lpt0) = subarray(avol0, m10, # lpt0), disk-layout(mksb(adr0, m0, m1, m2, m4, m5, m10), # lpt0), disk-layout(mksb(adr, m, m6, m7, m8, m9, m10), # lpt0), ebm-vol-inv(avol2), ebm-vol-inv(subarray(avol0, m10, # lpt0)), ebm-vol-inv(avol0), is-encoded(log, buf4), is-encoded(lpt0, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))), is-encoded(mksb(adr0, m0, m1, m2, m4, m5, m10), buf), is-encoded(lpt2, lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE))), is-encoded(plog, buf1), is-encoded(mksb(adr, m, m6, m7, m8, m9, m10), buf2), is-encoded-pad(ns, m4, buf0), is-encoded-pad(orphans1, m8, buf3), mapped-full?(avol2, m9, lptlebs(# lpt0, LEB_SIZE)), mapped-full?(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), logoff0 ≠ LEB_SIZE → # buf4 = logoff0, err ≠ ESUCCESS → mksb(adr, m, m6, m7, m8, m9, m10) = mksb(adr0, m0, m1, m2, m4, m5, m10) ∧ avol2[m1] = mapped(buf1) ∧ avol2[m2] = mapped(buf0) ∧ lebs(avol2, m5, lptlebs(# lpt0, LEB_SIZE)) = lebs(avol0, m5, lptlebs(# lpt0, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, err = ESUCCESS → adr = adr1 ∧ m = m3 ∧ buf4 = mkbuf(0) ∧ lpt0 = lpt ∧ orphans1 = ns0, err = ESUCCESS ∨ ⌊err⌋ ⊦ ⟨apersistence_io_commit#(lpt, adr1, m3, subarray(avol0, m10, # lpt0); ns0, adr0, m0, plog, lpt2, ns; err0)⟩ ( m0 = m ∧ adr0 = adr ∧ log = plog ∧ is-encoded(lpt2, lebs(avol2, m9, lptlebs(# lpt0, LEB_SIZE))) ∧ orphans1 = ns ∧ orphans0 = ns0 ∧ err = err0)

Rule argument

Additional information

Used simplifier rules: ⊦ is-encoded(lpt0, buf) ∧ # lpt0 = # lpt1 → (is-encoded(lpt1, buf) ↔ lpt0 = lpt1); (s)% ⊦ m ≤ m + n; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + n = m + n0 ↔ n = n0; (s)