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Proof step 53 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf), avol[m5] = mapped(buf1), buf3 = mkbuf(m2 * ENCODED_NAT_SIZE), err = err0, n = m2 * ENCODED_NAT_SIZE, n0 = 0, 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, logoff ≠ LEB_SIZE → # buf1 = logoff, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ err = ESUCCESS, ∀ buf1. # buf1 = # buf3 → range=(buf3, 0, buf1, 0, n0) → # buf3 ≥ n0 + n

Heuristic simplifier applied rule simplifier

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ ¬ n < n; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ n ≥ m ↔ m ≤ 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)% ⊦ 0 ≤ m; (s)% ⊦ range=(buf, n0, buf0, n1, 0) ↔ n0 ≤ # buf ∧ n1 ≤ # buf0; (s)% ⊦ # mkbuf(n) = n; (s)