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Proof step 44 from proof prepost-write-orphans (previous step)

avol = avol1[n, mapped(mkbuf(0))], err = err0, err = ESUCCESS, n < # avol1, ebm-vol-inv(avol1[n, mapped(mkbuf(0))]), ebm-vol-inv(avol1), is-aligned(# buf0, EB_PAGE_SIZE), is-encoded-pad(orphans0, # orphans0, buf0), # buf0 ≤ LEB_SIZE, ⌊err0⌋ ∨ err0 = ESUCCESS ⊦ [avol[n] := mapped(avol[n].data + mkempbuf(0 - # avol[n].data) + subarray(buf0, 0, # buf0))] ( ebm-vol-inv(avol) → (err = ESUCCESS ∨ ⌊err⌋ ) ∧ id○(avol, avol1, n) ∧ (err = ESUCCESS → avol[n].mapped? ∧ is-encoded-pad(orphans0, # orphans0, avol[n].data))), # buf0 = 0

Heuristic symbolic execution applied rule assign right

And closed the goal!

Rule argument

Additional information

Used simplifier rules: ⊦ m < # avol → avol[m, aleb][m] = aleb; (s)% ⊦ mapped(buf).data = buf; (s)% ⊦ # mkbuf(n) = n; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m ≤ m; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ mkbuf(0) + buf = buf; (s)% ⊦ mkempbuf(0) + buf = buf; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # avol ⊦ avol[m, aleb][m, aleb0] = avol[m, aleb0]; (s)% ⊦ # avol[n, aleb] = # avol; (s)% ⊦ mapped(buf).mapped?; (s)% ⊦ ¬ ⌊ESUCCESS⌋ ; (s)% ⊦ id○(avol[n, aleb], avol0, n) ↔ id○(avol, avol0, n); (s)% ⊦ id○(avol, avol, n); (ss)%⊦ is-encoded-pad(ns0, n, buf) → (is-encoded-pad(ns1, n, buf) ↔ ns0 = ns1); (s)