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Proof step 32 from proof prepost-read-superblock (previous step)

# buf3 + # buf2 = encoding-size(sb0, EB_PAGE_SIZE), LEB_SIZE = n0 + encoding-size(sb0, EB_PAGE_SIZE), avol[0] = mapped(buf3 + buf2), subarray((buf3 + buf2) + mkempbuf(n0), 0, encoding-size(sb, EB_PAGE_SIZE)) = buf0 + buf, ebm-vol-inv(avol), is-encoded-unaligned(sb0, buf3), is-encoded-unaligned(sb, buf0), encoding-size(sb0, EB_PAGE_SIZE) ≤ LEB_SIZE, encoding-size(sb, EB_PAGE_SIZE) ≤ LEB_SIZE ⊦ # avol = 0, sb = sb0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: array-splice, inst: buffer name: subarray-append-shift-right seq: ⊦ # buf ≤ m ∧ m ≤ # buf + # buf0 → subarray(buf + buf0, 0, m) = buf + subarray(buf0, 0, m - # buf) subst: [m, buf0, buf] → [encoding-size(sb, EB_PAGE_SIZE), mkempbuf(n0), buf3 + buf2] flags: <all paths>

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # mkempbuf(n) = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%⊦ buf0 + buf1 = buf2 + buf3 ∧ is-encoded-unaligned(sb, buf0) → (is-encoded-unaligned(sb0, buf2) ↔ # buf0 = # buf2 ∧ sb = sb0); (ws) Used terms: encoding-size(sb, EB_PAGE_SIZE), mkempbuf(n0), buf3 + buf2