[Imprint][Data Privacy Statement][E-Mail]

View long theorem info. View the proof. Back to main index. View the specification. View theorem base summary, View theorem base listing, the used properties by spec, the dependency list, the symbol table,

Proof step 50 from proof refine-read (previous step)

# buf5 = n3 + n2 + n1, # buf1 = # buf5, # avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf), avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), avol = subarray(avol0, m6, # lpt), buf0 = buf5, m = m9, m0 = m7, m1 = m8, n = n1, n0 = n2, ns = orphans, plog = log, 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-encoded(mksb(adr, m9, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), range=(buf5, 0, buf1, 0, n2), range=(buf5, n2 + n1, buf1, n2 + n1, n3), m6 + # lpt ≤ # avol0, n2 + n1 ≤ # buf5, m7 + n1 ≤ LEB_SIZE, m6 ≤ # avol0, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟨if m1 < # avol ∧ avol[m1].mapped? ∧ n0 + n ≤ # buf0 ∧ m0 + n ≤ LEB_SIZE then {fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), m0, buf0, n0, n) else choose buf with # buf = # buf0 ∧ range=(buf0, 0, buf, 0, n0) ∧ range=(buf0, n0 + n, buf, n0 + n, # buf0 - n0 + n) in buf0 := buf} else abort⟩ (buf1 = buf0 ∧ err0 = err)

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 51:
# buf5 = n3 + n2 + n1, # buf1 = # buf5, # avol0 = # lpt + m6, avol0[m6 + m8] = mapped(buf), avol0[0] = mapped(buf2), avol0[m3] = mapped(buf3), avol0[m2] = mapped(buf4), 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-encoded(mksb(adr, m9, m2, m3, m4, m5, m6), buf2), is-encoded(lpt, lebs(avol0, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf4), is-encoded-pad(orphans, m4, buf3), mapped-full?(avol0, m5, lptlebs(# lpt, LEB_SIZE)), range=(buf5, 0, buf1, 0, n2), range=(buf5, n2 + n1, buf1, n2 + n1, n3), n2 + n1 ≤ # buf5, m7 + n1 ≤ LEB_SIZE, m6 ≤ # avol0, ⌊err0⌋ , logoff ≠ LEB_SIZE → # buf4 = logoff ⊦ ⟨if subarray(avol0, m6, # lpt)[m8].mapped? then {fail_or_success#(; ; err); if err = ESUCCESS then buf5 := copy(subarray(avol0, m6, # lpt)[m8].data + mkempbuf(LEB_SIZE - # subarray(avol0, m6, # lpt)[m8].data), m7, buf5, n2, n1) else choose buf with # buf = # buf5 ∧ range=(buf5, 0, buf, 0, n2) ∧ range=(buf5, n2 + n1, buf, n2 + n1, # buf5 - n2 + n1) in buf5 := buf} else abort⟩ (buf1 = buf5 ∧ err0 = err)

Rule argument

Additional information

Used simplifier rules: ⊦ m ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # subarray(avol, m, n) = n; (s)