LEFTNEIGHBORS-declLEFTNEIGHBORS(x; ; lneighbors)
{lneighbors := [];
let xpos = 1, stack = []
in while xpos ≤ # x
do {/* _:
invariant xpos ≠ 0 ∧ xpos ≤ # x + 1 ∧ (stack = [] ↔ xpos = 1) ∧ ordered>(stack) ∧ bounded(stack, 1, xpos)
∧ lneighbors = leftneighbors(x, xpos - 1) ∧ valid-stack(stack, x) ∧ (stack ≠ [] → stack.head = xpos - 1)
wfbound # x + 1 - xpos;
*/;
while stack ≠ [] ∧ ¬ x[stack.head]! < x[xpos]!
do {/* _:
invariant xpos ≠ 0 ∧ xpos ≤ # x ∧ ordered>(stack) ∧ bounded(stack, 1, xpos) ∧ valid-stack(stack, x)
∧ leftneighbor(x, xpos - 1) = first-lower(stack, x, x[xpos]!)
wfbound # stack;
*/;
stack := stack.tail};
if stack = [] then lneighbors := lneighbors + 0 else lneighbors := lneighbors + stack.head; stack := xpos + stack; xpos := xpos + 1}
}
00LEFTNEIGHBORS-decl-proofLEFTNEIGHBORS-decl-proof-info
The proof is valid.
LEFTNEIGHBORS-correct