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Proof step 126 from proof inv-recover (previous step)

m8 + # lpt0 = # avol1, avol1[m10] = mapped(buf1), avol1[m5] = mapped(buf0), avol1[0] = mapped(buf2), m10 < # avol2, disk-layout(mksb(adr0, m9, m10, m5, m6, m7, m8), # lpt0), ebm-vol-inv(avol1), is-encoded(lpt0, lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE))), is-encoded(log0, buf1), is-encoded(mksb(adr0, m9, m10, m5, m6, m7, m8), buf2), is-encoded-pad(orphans0, m6, buf0), mapped-full?(avol1, m7, lptlebs(# lpt0, LEB_SIZE)), m7 + lptlebs(# lpt0, LEB_SIZE) ≤ # avol1, m8 ≤ # avol1, avol1 ⊆ avol2, m3 ≠ LEB_SIZE → # buf1 = m3 ⊦ # lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE)) = lptsize(# lpt0, LEB_SIZE)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: persistence-io-inv name: lebs-size-mappedfull seq: n + m < # avol ⊦ mapped-full?(avol, n, m) → # lebs(avol, n, m) = m * LEB_SIZE subst: [m, n, avol] → [lptlebs(# lpt0, LEB_SIZE), m7, avol1] flags: <all paths>

Additional information

Used simplifier rules: ⊦ lptlebs(n, LEB_SIZE) * LEB_SIZE = lptsize(n, LEB_SIZE) ↔ true; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult Used terms: lptlebs(# lpt0, LEB_SIZE), m7, avol1