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Proof step 58 from proof prepost-read-orphans (previous step)

m4 + # lpt = # avol, avol[0] = mapped(buf2), avol[m1] = mapped(buf3), avol[m5] = mapped(buf1), LEB_SIZE < m2 * ENCODED_NAT_SIZE, m1 < # avol, disk-layout(mksb(adr, m6, m5, m1, m2, m3, m4), # lpt), ebm-vol-inv(avol), is-encoded(log, buf1), is-encoded(lpt, lebs(avol, m3, lptlebs(# lpt, LEB_SIZE))), is-encoded(mksb(adr, m6, m5, m1, m2, m3, m4), buf2), is-encoded-pad(orphans0, m2, buf3), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff ⊦ m2 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 59:
⊦ is-encoded-pad(ns, n, buf) ↔ n = # ns ∧ (∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(ns, buf0))
Proof step 60:
m4 + # lpt = # avol, avol[m5] = mapped(buf1), avol[m1] = mapped(buf3), avol[0] = mapped(buf2), m2 = # orphans0, m1 < # avol, LEB_SIZE < m2 * ENCODED_NAT_SIZE, 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), mapped-full?(avol, m3, lptlebs(# lpt, LEB_SIZE)), logoff ≠ LEB_SIZE → # buf1 = logoff, ∃ buf0, buf1. is-aligned(# buf3, EB_PAGE_SIZE) ∧ buf3 = buf0 + buf1 ∧ is-encoded(orphans0, buf0) ⊦ m2 = 0

Rule argument

spec: encoding-orphans name: is-encoded-pad seq: ⊦ is-encoded-pad(ns, n, buf) ↔ n = # ns ∧ (∃ buf0, buf1. is-aligned(# buf, EB_PAGE_SIZE) ∧ buf = buf0 + buf1 ∧ is-encoded(ns, buf0)) subst: [buf, n, ns] → [buf3, m2, orphans0] flags: <all paths>

Additional information

Used terms: buf3, m2, orphans0