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Proof step 14 from proof abs-nodes-at-least-flashsize (previous step)

# buf1 + # buf0 < (2 * NODE_HEADER_SIZE + nd.alignedsize) + x0.flashsize, abs-nodes(buf0, m + # buf1, nd ' + x0, @(m0, m1) ' + lax0, false), abs-padding(buf1), ∀ buf2, x, m, lax. # buf2 < #(buf1 + buf0) → # buf2 < x.flashsize ∧ abs-nodes(buf2, m, x, lax, false) → x = [] ⊦

User applied rule apply induction

And closed the goal!

Rule argument

subst: [buf2, x, m, lax] → [buf0, nd ' + x0, m + # buf1, @(m0, m1) ' + lax0]

Additional information

Used simplifier rules: size-rec: ⊦ (a ' + x).flashsize = a.flashsize + x.flashsize;%abs-nodes-unique-strong-h: ⊦ abs-nodes(buf, m, x0, lax0, false) → (abs-nodes(buf, m, x1, lax1, boolvar1) ↔ x0 = x1 ∧ lax0 = lax1);% ⊦ x + y = [] ↔ x = [] ∧ y = []; (as)% ⊦ a ' ≠ []; (s)%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ nd.flashsize = 2 * NODE_HEADER_SIZE + nd.alignedsize; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ ¬ m < n → ¬ m + m0 < n; (s)% ⊦ #(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)% ⊦ # mkbuf(n) = n; (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s) Used terms: buf0, nd ' + x0, m + # buf1, @(m0, m1) ' + lax0