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Proof step 129 from proof inv-recover (previous step)

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

Proof step 130:
⊦ disk-layout(sb, mainareasize) ↔ ( sb.log = SB_LOG ∧ sb.orph = SB_ORPH ∧ sb.lpt = SB_LPT ∨ sb.log = SB_LOG + 1 ∧ sb.orph = SB_ORPH + 1 ∧ sb.lpt = SB_LPT + lptlebs(mainareasize, LEB_SIZE)) ∧ sb.main = SB_LPT + 2 * lptlebs(mainareasize, LEB_SIZE)
Proof step 131:
m8 + # lpt0 = # avol1, m7 + lptlebs(# lpt0, LEB_SIZE) = # avol1, mksb(adr0, m9, m10, m5, m6, m7, m8).main = SB_LPT + 2 * lptlebs(# lpt0, LEB_SIZE), avol1[m10] = mapped(buf1), avol1[m5] = mapped(buf0), avol1[0] = mapped(buf2), m10 < # avol2, 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)), m8 ≤ # avol1, avol1 ⊆ avol2, m3 ≠ LEB_SIZE → # buf1 = m3, mksb(adr0, m9, m10, m5, m6, m7, m8).log = SB_LOG ∧ mksb(adr0, m9, m10, m5, m6, m7, m8).orph = SB_ORPH ∧ mksb(adr0, m9, m10, m5, m6, m7, m8).lpt = SB_LPT ∨ mksb(adr0, m9, m10, m5, m6, m7, m8).log = SB_LOG + 1 ∧ mksb(adr0, m9, m10, m5, m6, m7, m8).orph = SB_ORPH + 1 ∧ mksb(adr0, m9, m10, m5, m6, m7, m8).lpt = SB_LPT + lptlebs(# lpt0, LEB_SIZE) ⊦ # lebs(avol1, m7, lptlebs(# lpt0, LEB_SIZE)) = lptsize(# lpt0, LEB_SIZE)

Rule argument

spec: persistence-io-inv name: disk-layout seq: ⊦ disk-layout(sb, mainareasize) ↔ ( sb.log = SB_LOG ∧ sb.orph = SB_ORPH ∧ sb.lpt = SB_LPT ∨ sb.log = SB_LOG + 1 ∧ sb.orph = SB_ORPH + 1 ∧ sb.lpt = SB_LPT + lptlebs(mainareasize, LEB_SIZE)) ∧ sb.main = SB_LPT + 2 * lptlebs(mainareasize, LEB_SIZE) subst: [mainareasize, sb] → [# lpt0, mksb(adr0, m9, m10, m5, m6, m7, m8)] flags: <all paths>

Additional information

Used terms: # lpt0, mksb(adr0, m9, m10, m5, m6, m7, m8)