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Proof step 20 from proof refine-remap (previous step)

# avol0 = # lpt + m5, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol = avol0, avol1 = subarray(avol0, m5, # lpt), err = ESUCCESS, err = err0, m6 < # lpt, m5 + m6 < # avol, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt)), is-encoded(log, buf1), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, m5 + # lpt ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨apersistence_io_remap#(m6, adr, m0, log, lpt, orphans; avol1; err1)⟩ ( # avol[m5 + m6, mapped(mkbuf(0))] = m5 + (# avol[m5 + m6, mapped(mkbuf(0))] - m5) ∧ avol1 = subarray(avol[m5 + m6, mapped(mkbuf(0))], m5, # avol[m5 + m6, mapped(mkbuf(0))] - m5) ∧ is-encoded(log, avol[m5 + m6, mapped(mkbuf(0))][m1].data) ∧ is-encoded(lpt, lebs(avol[m5 + m6, mapped(mkbuf(0))], m4, lptlebs(# avol[m5 + m6, mapped(mkbuf(0))] - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol[m5 + m6, mapped(mkbuf(0))][m2].data) ∧ err = err1)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
# avol0 = # lpt + m5, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol1 = subarray(avol0, m5, # lpt), m6 < # lpt, disk-layout(mksb(adr, m0, m1, m2, m3, m4, m5), # lpt), ebm-vol-inv(avol0), ebm-vol-inv(subarray(avol0, m5, # lpt)), is-encoded(log, buf1), is-encoded(lpt, lebs(avol0, m4, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m0, m1, m2, m3, m4, m5), buf), is-encoded-pad(orphans, m3, buf0), mapped-full?(avol0, m4, lptlebs(# lpt, LEB_SIZE)), m5 ≤ # avol0, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟨apersistence_io_remap#(m6, adr, m0, log, lpt, orphans; avol1; err1)⟩ ( avol1 = subarray(avol0[m5 + m6, mapped(mkbuf(0))], m5, # avol0 - m5) ∧ is-encoded(log, avol0[m5 + m6, mapped(mkbuf(0))][m1].data) ∧ is-encoded(lpt, lebs(avol0[m5 + m6, mapped(mkbuf(0))], m4, lptlebs(# avol0 - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol0[m2].data) ∧ ESUCCESS = err1)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%m ≠ n ⊦ avol[m, aleb][n] = avol[n]; (s)%⊦ disk-layout(mksb(adr, m0, m1, m2, m, m3, m4), mainareasize) → m4 + n ≠ m2; (s)%n ≤ m ⊦ (m - n) + n0 = n1 ↔ m + n0 = n + n1; (s)% ⊦ m ≤ n → (n < m ↔ false); (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ m = m0 + n0 ∧ n < n0 → m0 + n < m; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic