[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 8 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf0), avol[m0] = mapped(buf1), buf = mkbuf(m2 * ENCODED_NAT_SIZE), disk-layout(mksb(adr, m, m0, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m, m0, m1, m2, m3, m4), buf2), is-encoded-pad(orphans0, m2, buf0), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪ebm_avol_read#(m1, 0, 0, m2 * ENCODED_NAT_SIZE, avol; buf; err); if err = ESUCCESS then persistence_io_decode_orphans#(m2, buf; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Heuristic nonrecursive calls applied rule call right

And obtained the following new goals

Proof step 9:
m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf3), avol[0] = mapped(buf2), buf = mkbuf(m2 * ENCODED_NAT_SIZE), buf0 = buf, m = 0, m0 = m1, n = m2 * ENCODED_NAT_SIZE, n0 = 0, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf1), is-encoded-pad(orphans0, m2, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪if m0 < # avol ∧ avol[m0].mapped? ∧ n0 + n ≤ # buf0 ∧ m + n ≤ LEB_SIZE then {fail_or_success#(; ; err); if err = ESUCCESS then buf0 := copy(avol[m0].data + mkempbuf(LEB_SIZE - # avol[m0].data), m, 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; if err = ESUCCESS then persistence_io_decode_orphans#(m2, buf0; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Rule argument

pos: right 1

Additional information

Used simplifier rules: ebm_avol_read#(LNUM, OFFSET, N0, N, AVOL; BUF; ERR) {if LNUM < # AVOL ∧ AVOL[LNUM].mapped? ∧ N0 + N ≤ # BUF ∧ OFFSET + N ≤ LEB_SIZE then {fail_or_success#(; ; ERR); if ERR = ESUCCESS then BUF := copy ( AVOL[LNUM].data + mkempbuf(LEB_SIZE - # AVOL[LNUM].data), OFFSET, BUF, N0, N) else choose BUF0 with # BUF0 = # BUF ∧ range=(BUF, 0, BUF0, 0, N0) ∧ range=(BUF, N0 + N, BUF0, N0 + N, # BUF - N0 + N) in BUF := BUF0} else abort };