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Proof step 131 from proof inv-commit (previous step)

# avol = # avol0, # buf3 = lptsize(# lpt, LEB_SIZE), # lpt0 = # lpt, # buf3 = lptlebs(# lpt, LEB_SIZE) * LEB_SIZE, (5 + 2 * lptlebs(# lpt, LEB_SIZE)) + # lpt = # avol0, avol0[0] = mapped(buf2), avol0[3] = mapped(buf0), avol0[1] = mapped(buf1), 4 < # avol0, 2 < # avol0, ebm-vol-inv(avol), ebm-vol-inv(avol0[2, mapped(mkbuf(0))]), ebm-vol-inv(avol0), ebm-vol-inv(avol0[2, mapped(mkbuf(0))][4, mapped(buf)]), is-encoded(lpt, buf3), is-encoded(log, buf1), is-encoded(lpt0, lebs(avol0, 5, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr0, m2, 1, 3, m6, 5, 5 + 2 * lptlebs(# lpt, LEB_SIZE)), buf2), is-encoded-pad(orphans0, m6, buf0), is-encoded-pad(orphans, # orphans, buf), mapped-full?(avol0, 5, lptlebs(# lpt, LEB_SIZE)), range=(avol, 0, avol0[2, mapped(mkbuf(0))][4, mapped(buf)], 0, 5 + lptlebs(# lpt, LEB_SIZE)), range=(avol, 5 + 2 * lptlebs(# lpt, LEB_SIZE), avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE), # lpt), 2 * lptlebs(# lpt, LEB_SIZE) + 5 ≤ # avol0, 5 + 2 * lptlebs(# lpt, LEB_SIZE) ≤ # avol0, ⌊err⌋ , logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ mapped-full?(avol, 5, lptlebs(# lpt, LEB_SIZE))

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-io-inv name: mapped-full-range-eq seq: m ≤ n0, n0 + n1 ≤ m + m2 ⊦ range=(avol0, m, avol1, m, m2) ∧ mapped-full?(avol1, n0, n1) → mapped-full?(avol0, n0, n1) subst: [m, m2, avol1, n1, n0, avol0] → [0, 5 + lptlebs(# lpt, LEB_SIZE), avol0[2, mapped(mkbuf(0))][4, mapped(buf)], lptlebs(# lpt, LEB_SIZE), 5, avol] flags: <all paths>

Additional information

Used simplifier rules: a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)% ⊦ m ≤ m; (s)%n0 < n ⊦ mapped-full?(avol[n0, aleb], n, m) ↔ mapped-full?(avol, n, m); (s) Used terms: 0, 5 + lptlebs(# lpt, LEB_SIZE), avol0[2, mapped(mkbuf(0))][4, mapped(buf)], lptlebs(# lpt, LEB_SIZE), 5, avol