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Proof step 27 from proof prepost-read-superblock (previous step)

LEB_SIZE = n0 + # buf1, avol[0] = mapped(buf1), subarray(buf1 + mkempbuf(n0), 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, ebm-vol-inv(avol), is-encoded(sb0, buf1), is-encoded-unaligned(sb, buf0), encoding-size(sb, EB_PAGE_SIZE) ≤ LEB_SIZE, # buf1 ≤ LEB_SIZE ⊦ # avol = 0, sb = sb0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 28:
⊦ is-encoded(sb, buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded-unaligned(sb, buf0) ∧ # buf = encoding-size(sb, EB_PAGE_SIZE))
Proof step 29:
LEB_SIZE = n0 + # buf1, avol[0] = mapped(buf1), subarray(buf1 + mkempbuf(n0), 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, ebm-vol-inv(avol), is-encoded-unaligned(sb, buf0), # buf1 ≤ LEB_SIZE, encoding-size(sb, EB_PAGE_SIZE) ≤ LEB_SIZE, ∃ buf0, buf2. buf1 = buf0 + buf2 ∧ is-encoded-unaligned(sb0, buf0) ∧ # buf1 = encoding-size(sb0, EB_PAGE_SIZE) ⊦ # avol = 0, sb = sb0

Rule argument

spec: encoding-aligned, inst: encoding-superblock name: is-encoded-aligned seq: ⊦ is-encoded(sb, buf) ↔ (∃ buf0, buf1. buf = buf0 + buf1 ∧ is-encoded-unaligned(sb, buf0) ∧ # buf = encoding-size(sb, EB_PAGE_SIZE)) subst: [buf, sb] → [buf1, sb0] flags: <all paths>

Additional information

Used terms: buf1, sb0