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Proof step 127 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⌋ ⊦ 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)])[m2], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 128:
⊦ n < # evol → abs(evol)[n] = abs(evol[n])
Proof step 129:
LEB_SIZE = (n5 + n0) + n1 + n4, avols[default-volid][m2] = mapped(buf0, n4), m2 < # avols[default-volid], n0 < n, m2 < # avols[default-volid][m2, mapped(subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0)], 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⌋ ⊦ 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)][m2]), n0 = 0

Rule argument

spec: ebm-vol-abs name: abs-at seq: ⊦ n < # evol → abs(evol)[n] = abs(evol[n]) subst: [n, evol] → [m2, avols[default-volid] [m2, mapped ( subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0) ]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ v ∈ avols ∧ m < # avols[v] ∧ avols[v][m] = mapped(buf, m0) ∧ ebm-cons(avols) → # buf = LEB_SIZE; (s)% ⊦ m ≠ n → (m ≤ n ↔ m < n); (s)% ⊦ # evol[n, leb] = # evol; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer] Used terms: m2, avols[default-volid] [m2, mapped (subarray(buf0, 0, n1 + n4) + subarray(buf, n3, n0) + mkempbuf(n5), (n1 + n4) + n0) ]