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Proof step 20 from proof abs-nodes-emptyheader-h (previous step)

lax.head = @(m0, m1), isempty(buf1 + buf0, 0, NODE_HEADER_SIZE), abs-padding(buf1) ∧ abs-nodes(buf0, m + # buf1, nd ' + x0, lax, weak) ∨ lax ≠ [] ∧ m0 = m ∧ m1 = # buf1 ∧ abs-node(buf1, nd) ∧ abs-nodes(buf0, m + # buf1, x0, lax.tail, weak) ⊦

User applied rule case distinction

And obtained the following new goals

Proof step 21:
lax.head = @(m0, m1), m0 = m, m1 = # buf1, abs-node(buf1, nd), abs-nodes(buf0, m + # buf1, x0, lax.tail, weak), isempty(buf1 + buf0, 0, NODE_HEADER_SIZE) ⊦ lax = []

Rule argument

pos: left 3

Additional information

Used simplifier rules: abs-nodes-first-adr-explicit: ⊦ abs-nodes(buf, m, a ' + x, lax, weak) → (lax.head = ladr ↔ (∃ lax0. lax = ladr + lax0));%abs-nodes-mkbuf0-empty-h: ⊦ abs-nodes(mkbuf(0), m, x, lax, weak) ↔ x = [] ∧ lax = [];%abs-nodes-headerspace: # buf ≠ 0 ⊦ abs-nodes(buf, m, x, lax, weak) → (NODE_HEADER_SIZE ≤ # buf + n ↔ NODE_HEADER_SIZE ≤ # buf);%abs-nodes-nospace-h: # buf < NODE_HEADER_SIZE ⊦ abs-nodes(buf, m, x, lax, boolvar) ↔ x = [] ∧ lax = [] ∧ buf = mkbuf(0);%a: ⊦ (x + y) + z = x + y + z; from specification list% ⊦ ladr + lax = ladr ' + lax; (s)% ⊦ n + 0 = n; (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ # buf = 0 ↔ buf = mkbuf(0); (s)% ⊦ a ' + x ≠ []; (s)% ⊦ m ≤ n ↔ ¬ n < m; (ss)% ⊦ # buf < NODE_HEADER_SIZE → ¬ abs-padding(buf); (s)%n + m ≤ # buf0, n + m ≤ # buf0 + # buf1 ⊦ isempty(buf0 + buf1, n, m) ↔ isempty(buf0, n, m); (s)%append-a: ⊦ (buf + buf0) + buf1 = buf + buf0 + buf1; from specification array-splice[buffer]% ⊦ isempty(buf, 0, NODE_HEADER_SIZE) → ¬ abs-padding(buf); (s)