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Proof step 20 from proof ls-datasize-wear-level (previous step)

LEB_SIZE = n1 + m, LEB_SIZE = n0 + m, subarray(buf, m, n1) = mkempbuf(n1), m < datasize(subarray(buf, 0, m) + subarray(buf, m, n1), LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE ⊦ ∃ buf0. subarray(buf, m, n1) = mkempbuf(n0) + buf0, ∃ buf0. subarray(buf, 0, m) + subarray(buf, m, n1) = mkempbuf(LEB_SIZE) + buf0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 21:
LEB_SIZE = n0 + m, subarray(buf, m, n0) = mkempbuf(n0), m < datasize(subarray(buf, 0, m) + subarray(buf, m, n0), LEB_SIZE), is-aligned(m, EB_PAGE_SIZE), m ≤ LEB_SIZE ⊦ ∃ buf0. subarray(buf, 0, m) + subarray(buf, m, n0) = mkempbuf(LEB_SIZE) + buf0, ∃ buf0. # buf0 = 0

Rule argument

Additional information

Used simplifier rules: ls-datasize-zero: n ≤ # buf ⊦ datasize(buf, n) = 0 ↔ (∃ buf0. buf = mkempbuf(n) + buf0);% ⊦ buf + buf0 = buf ↔ # buf0 = 0; (s)% ⊦ ¬ n < n; (s)% ⊦ LEB_SIZE ≠ 0; (s)%lf-01: ⊦ m < n ∧ n = n0 → m < n0; (forward) from specification nat-basic%lf-02: ⊦ m < n ∧ m = n0 → n0 < n; (forward) from specification nat-basic% ⊦ m ≤ n ↔ ¬ n < m; (ss)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ # subarray(buf, m, n) = n; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%f: ⊦ m < n → n ≠ 0; (forward) from specification nat-basic%eqs: ⊦ m = n + n0 ∧ m = n + n1 → n0 = n1; (forward) from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic