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Proof step 25 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, LEB_SIZE = n0 + # buf, avol[0] = mapped(buf2), avol[m1] = mapped(buf), avol[m5] = mapped(buf1), 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, # buf ≤ LEB_SIZE, 0 + m2 * ENCODED_NAT_SIZE ≤ #(avol[m1].data + mkempbuf(n0)), 0 + m2 * ENCODED_NAT_SIZE ≤ # mkbuf(m2 * ENCODED_NAT_SIZE), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_decode_orphans# (m2, subarray(mkbuf(m2 * ENCODED_NAT_SIZE), 0, 0) + subarray(avol[m1].data + mkempbuf(n0), 0, m2 * ENCODED_NAT_SIZE) + subarray(mkbuf(m2 * ENCODED_NAT_SIZE), 0 + m2 * ENCODED_NAT_SIZE, # mkbuf(m2 * ENCODED_NAT_SIZE) - 0 - m2 * ENCODED_NAT_SIZE) ; ; orphans, err0)⟫ ((err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → orphans = orphans0))

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 26:
m4 + # lpt = # avol, LEB_SIZE = n0 + # buf, avol[0] = mapped(buf2), avol[m1] = mapped(buf), avol[m5] = mapped(buf1), 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)), # buf ≤ LEB_SIZE, m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_decode_orphans# (m2, subarray(mkbuf(m2 * ENCODED_NAT_SIZE), 0, 0) + subarray(avol[m1].data + mkempbuf(n0), 0, m2 * ENCODED_NAT_SIZE) + subarray(mkbuf(m2 * ENCODED_NAT_SIZE), m2 * ENCODED_NAT_SIZE, 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)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)% ⊦ m ≤ m; (s)% ⊦ # mkbuf(n) = n; (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)