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Proof step 57 from proof refine-remap (previous step)

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

Heuristic symbolic execution applied rule assign right

And obtained the following new goals

Proof step 58:
# avol0 = # lpt + m5, avol0[m1] = mapped(buf1), avol0[m2] = mapped(buf0), avol0[0] = mapped(buf), avol = avol0, err = err0, m5 + m6 < # avol, 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, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟨avol1 := subarray(avol0, m5, # lpt); apersistence_io_remap#(m6, adr, m0, log, lpt, orphans; avol1; err1)⟩ ( # avol[m5 + m6, unmapped] = m5 + (# avol[m5 + m6, unmapped] - m5) ∧ avol1 = subarray(avol[m5 + m6, unmapped], m5, # avol[m5 + m6, unmapped] - m5) ∧ is-encoded(log, avol[m5 + m6, unmapped][m1].data) ∧ is-encoded(lpt, lebs(avol[m5 + m6, unmapped], m4, lptlebs(# avol[m5 + m6, unmapped] - m5, LEB_SIZE))) ∧ is-encoded-pad(orphans, m3, avol[m5 + m6, unmapped][m2].data) ∧ err = err1), err = ESUCCESS

Rule argument

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)