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Proof step 37 from proof abs-nodes-crash-h (previous step)

abs-nodes(buf1, m + # buf0, [], [], true), abs-padding(buf0), is-aligned(n0 + # buf0, NODE_HEADER_SIZE), n0 ≤ # buf1, ∀ buf2, m, x, lax, n. # buf2 < #(buf0 + buf1) → abs-nodes(buf2, m, x, lax, true) ∧ is-aligned(n, NODE_HEADER_SIZE) ∧ n ≤ # buf2 → (∃ x0, lax0. x0 ⊑ x ∧ lax0 ⊑ lax ∧ abs-nodes(subarray(buf2, 0, n), m, x0, lax0, true)) ⊦ abs-nodes(subarray(buf1, 0, n0), m + # buf0, [], [], true)

User applied rule apply induction

And obtained the following new goals

Rule argument

subst: [buf2, m, x, lax, n] → [buf1, m + # buf0, [], [], n0]

Additional information

Used simplifier rules: abs-nodes-nospace-h: # buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, x, lax, boolvar) ↔ x = [] ∧ lax = [] ∧ buf = mkbuf(0);%abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];% ⊦ x ⊑ [] ↔ x = []; (s)% ⊦ lax ⊑ [] ↔ lax = []; (s)% ⊦ NODE_HEADER_SIZE ≠ 0; (s)%m ≠ 0, is-aligned(n1, m) ⊦ is-aligned(n0 + n1, m) ↔ is-aligned(n0, m); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ # mkbuf(n) = n; (s)% ⊦ m ≤ 0 ↔ m = 0; (s)%# buf = n ⊦ subarray(buf, 0, n) = buf; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)% ⊦ #(buf + buf0) = # buf + # buf0; (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ m + m0 ≤ m ↔ m0 = 0; (s)% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)%n ≠ 0 ⊦ is-aligned(0, n); (s)% ⊦ n + 0 = n; (s)% ⊦ ¬ abs-padding(mkbuf(0)); (s) Used terms: buf1, m + # buf0, [], [], n0