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Proof step 121 from proof refine-write (previous step)

LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), n0 < n, m2 < # avols[default-volid], ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n0, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n1, EB_PAGE_SIZE), default-volid ∈ avols, n0 + n1 + n4 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n1 + n4 ≤ LEB_SIZE, n4 ≤ LEB_SIZE, n3 + n ≤ # buf, (n1 + n4) + n ≤ LEB_SIZE, ⌊err1⌋ ⊦ abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0))] = abs(avols[default-volid][m2, mapped(subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0)]), n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 122:
⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n])
Proof step 123:
LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), m2 < # avols[default-volid], n0 < n, ebm-cons(avols), ebm-vol-inv(abs(avols[default-volid])), is-aligned(n1, EB_PAGE_SIZE), is-aligned(n, EB_PAGE_SIZE), is-aligned(n0, EB_PAGE_SIZE), default-volid ∈ avols, (n1 + n4) + n ≤ LEB_SIZE, n3 + n ≤ # buf, n4 ≤ LEB_SIZE, n1 + n4 ≤ LEB_SIZE, n3 + n0 ≤ # buf, n0 + n1 + n4 ≤ LEB_SIZE, ⌊err1⌋ ⊦ n0 = 0, # abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0))] = # abs(avols[default-volid][m2, mapped(subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0)]) ∧ (∀ n. n < # abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0))] → abs(avols[default-volid])[m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0))][n] = abs(avols[default-volid][m2, mapped(subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0)])[n])

Rule argument

spec: array, inst: avolume name: Extension seq: ⊦ avol = avol0 ↔ # avol = # avol0 ∧ (∀ n. n < # avol → avol[n] = avol0[n]) subst: [avol0, avol] → [abs (avols[default-volid] [m2, mapped ( subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0) ]), abs(avols[default-volid]) [m2, mapped ( subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0)) ]] flags: <all paths>

Additional information

Used terms: abs (avols[default-volid] [m2, mapped (subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0) ]), abs(avols[default-volid]) [m2, mapped(subarray(buf0, 0, n4) + mkempbuf(n1) + subarray(buf, n3, n0)) ]