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Proof step 34 from proof prepost-encode-orphans (previous step)

buf0 = mkbuf(align↑(# orphans2 * ENCODED_NAT_SIZE, m2)), err0 = ESUCCESS, m1 = LEB_SIZE, m2 = EB_PAGE_SIZE, m4 = 0, orphans0 = orphans2, is-aligned(# buf, m2), # buf ≤ m1, orphans ⊆ orphans2, err = ESUCCESS → m0 + # orphans * ENCODED_NAT_SIZE ≤ # buf ∧ is-encoded(orphans2 \ orphans, subarray(buf, 0, m0)), err = ESUCCESS ∨ ⌊err⌋ ⊦ # orphans2 * ENCODED_NAT_SIZE > m1, (err = ESUCCESS ∨ ⌊err⌋ ) ∧ (err = ESUCCESS → is-encoded-pad(orphans0, # orphans0, buf) ∧ # buf ≤ LEB_SIZE), err = ESUCCESS ∧ orphans ≠ ∅

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 35:
is-aligned(# buf, EB_PAGE_SIZE), is-encoded(orphans2, subarray(buf, 0, m0)), # orphans2 * ENCODED_NAT_SIZE ≤ LEB_SIZE, # buf ≤ LEB_SIZE, m0 ≤ # buf, m0 ≤ LEB_SIZE ⊦ is-encoded-pad(orphans2, # orphans2, buf)

Rule argument

Additional information

Used simplifier rules: ⊦ ∅ ⊆ ns; (s)% ⊦ ns \ ∅ = ns; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ n + 0 = n; (s)%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ 0 * n = 0; (s)% ⊦ # ∅ = 0; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m > n ↔ n < m; (s)