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Proof step 3 from proof inv-read (previous step)

sb.main + # lpt = # avol, avol[sb.main + m] = mapped(buf0), avol[0] = mapped(buf1), avol[sb.orph] = mapped(buf2), avol[sb.log] = mapped(buf3), m < # lpt, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(log, buf3), is-encoded(lpt, lebs(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE))), is-encoded(sb, buf1), is-encoded-pad(orphans, sb.orphsize, buf2), mapped-full?(avol, sb.lpt, lptlebs(# lpt, LEB_SIZE)), n + n0 ≤ # buf, m0 + n0 ≤ LEB_SIZE, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, sb, avol; buf; err)⟫ true

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 4:
m6 + # lpt = # avol, avol[m2] = mapped(buf3), avol[m3] = mapped(buf2), avol[0] = mapped(buf1), avol[m6 + m] = mapped(buf0), sb = mksb(adr, m1, m2, m3, m4, m5, m6), m < # lpt, disk-layout(sb, # lpt), ebm-vol-inv(avol), is-encoded(sb, buf1), is-encoded(lpt, lebs(avol, m5, lptlebs(# lpt, LEB_SIZE))), is-encoded(log, buf3), is-encoded-pad(orphans, m4, buf2), mapped-full?(avol, m5, lptlebs(# lpt, LEB_SIZE)), m0 + n0 ≤ LEB_SIZE, n + n0 ≤ # buf, logoff ≠ LEB_SIZE → # buf3 = logoff ⊦ ⟪persistence_io_read#(m, m0, n, n0, sb, avol; buf; err)⟫ true

Rule argument

spec: superblock name: elim seq: ⊦ ( ( ( ( (adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4) subst: [sb, adr, m, m0, m1, m2, m3, m4] → [sb, adr, m1, m2, m3, m4, m5, m6]

Additional information

Used simplifier rules: ⊦ ( ( ( ((adr = sb.indexaddr ∧ m = sb.maxino) ∧ m0 = sb.log) ∧ m1 = sb.orph) ∧ m2 = sb.orphsize) ∧ m3 = sb.lpt) ∧ m4 = sb.main ↔ sb = mksb(adr, m, m0, m1, m2, m3, m4); (elim) Used terms: sb, adr, m1, m2, m3, m4, m5, m6