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Proof step 11 from proof abs-nodes-aligned-headersize-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], weak), abs-padding(buf0), ∀ buf2, m, x, lax, weak. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, weak) → is-aligned(# buf2, NODE_HEADER_SIZE) ⊦ is-aligned(# buf0 + # buf1, NODE_HEADER_SIZE)

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [buf2, m, x, lax, weak] → [buf1, m + # buf0, [], [], weak]

Additional information

Used simplifier rules: ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ NODE_HEADER_SIZE ≠ 0; (s)% ⊦ # mkbuf(n) = n; (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s) Used terms: buf1, m + # buf0, [], [], weak