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Proof step 21 from proof prepost-read-orphans (previous step)

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)), # buf ≤ LEB_SIZE, 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))

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
m4 + # lpt = # avol, LEB_SIZE = n0 + # buf, LEB_SIZE = n1 + # avol[m1].data, 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, # avol[m1].data ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ ⟪persistence_io_decode_orphans# (m2, copy(avol[m1].data + mkempbuf(n1), 0, mkbuf(m2 * ENCODED_NAT_SIZE), 0, m2 * ENCODED_NAT_SIZE); ; orphans, err0)⟫ ((err0 = ESUCCESS ∨ ⌊err0⌋ ) ∧ (err0 = ESUCCESS → orphans = orphans0))

Rule argument

spec: nat name: elim-sub seq: n ≤ m ⊦ n0 = m - n ↔ m = n0 + n subst: [n, m, n0] → [# avol[m1].data, LEB_SIZE, n]

Additional information

Used simplifier rules: ⊦ m ≤ n ↔ ¬ n < m; (ss)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic%fle-01: ⊦ m ≤ n ∧ n < n0 → m < n0; (forward) from specification nat% ⊦ mapped(buf).data = buf; (s)% ⊦ ¬ m + n < m; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%n ≤ m ⊦ n0 = m - n ↔ m = n0 + n; (elim) Used terms: # avol[m1].data, LEB_SIZE, n