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Proof step 26 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)), # 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))

User applied rule insert program lemma

And obtained the following new goals

Proof step 27:
is-encoded(orphans0, buf), n = # orphans0, # buf = # orphans0 * ENCODED_NAT_SIZE ⊦ ⟪persistence_io_decode_orphans#(n, buf; ; orphans, err)⟫ ((err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0))
Proof step 28:
m4 + # lpt = # avol, LEB_SIZE = n0 + # buf, 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)), m2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, # buf ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ is-encoded (orphans0, 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)) ∧ m2 = # orphans0 ∧ # ( 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)) = # orphans0 * ENCODED_NAT_SIZE

Rule argument

spec: <toplevel> name: prepost-decode-orphans seq: is-encoded(orphans0, buf), n = # orphans0, # buf = # orphans0 * ENCODED_NAT_SIZE ⊦ ⟪persistence_io_decode_orphans#(n, buf; ; orphans, err)⟫ ( (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → orphans = orphans0)) subst: [buf, n, err, orphans, orphans0] → [ 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), m2, err0, orphans, orphans0] flags: <all paths>

Additional information

Used simplifier rules: ⊦ subarray(buf, n, 0) = mkbuf(0); (s)% ⊦ m - 0 = m; (s)% ⊦ m - m = 0; (s)% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ buf + mkbuf(0) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)