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Proof step 18 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf), avol[0] = mapped(buf2), buf3 = mkbuf(m2 * ENCODED_NAT_SIZE), err = ESUCCESS, err = err0, avol[m1].mapped?, m1 < # avol, disk-layout(mksb(adr, m6, m5, 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, m6, m5, m1, m2, m3, m4), buf2), is-encoded-pad(orphans0, m2, buf), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, 0 + m2 * ENCODED_NAT_SIZE ≤ # buf3, 0 + m2 * ENCODED_NAT_SIZE ≤ #(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data)), LEB_SIZE ≥ # avol[m1].data, logoff ≠ LEB_SIZE → # buf1 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ ⟪persistence_io_decode_orphans# (m2, copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), 0, buf3, 0, m2 * ENCODED_NAT_SIZE); ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 19:
m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf), avol[0] = mapped(buf2), m1 < # avol, 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, buf), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), # buf ≤ LEB_SIZE, m2 * ENCODED_NAT_SIZE ≤ # buf + (LEB_SIZE - # buf), m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_decode_orphans# (m2, copy(avol[m1].data + mkempbuf(LEB_SIZE - # avol[m1].data), 0, mkbuf(m2 * ENCODED_NAT_SIZE), 0, m2 * ENCODED_NAT_SIZE); ; orphans, err0)⟫ ((err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → orphans = orphans0))

Rule argument

Additional information

Used simplifier rules: ⊦ mapped(buf).data = buf; (s)% ⊦ mapped(buf) = mapped(buf0) ↔ buf = buf0; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ aleb.mapped? ↔ (∃ buf. aleb = mapped(buf)); (as)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)% ⊦ n ≥ m ↔ m ≤ n; (s)