sum

x / y

\(\mathtt {sum}(x, y)\) for \(x>y\) defined as \(x + \mathtt {sum}(x+1, y)\) or \(y + \mathtt {sum}(x, y1)\)

all / geq / leq

the conjecture holds for all x, y where \(x \le y\), or only for \(x \le y = c\), or only for \(c = x \le y\); where \(c\in \mathbb Z\) is an interpreted constant

val

declared / defined

\(\mathtt {val}\) was either not defined, only declared and axiomatized (as in (6)), or defined as a total computable function (as in (14))

inter / unint / mixed

the axiom and conjecture use concrete interpreted constants, or uninterpreted constants, or a mix of both

axfin/axall/ axleq/axgeq

the axiom holds for integers in an interval \([c, c')\), or for all \(x\in \mathbb Z\), or only for \(x \le c\), or only for \(x \ge c\); where \(c, c'\in \mathbb Z\) are constants

conjfin/conjall/conjleq /conjgeq

the conjecture holds for integers in an interval \([c, c']\), or for all integers, or only for integers \(\le c\), or only for integers \(\ge c\); where \(c, c' \in \mathbb Z\) are constants

power

0 / 1

\(\mathtt {power}\) defined starting with \(\mathtt {power}(x, 0) = 1\) or \(\mathtt {power}(x, 1) = x\)

all / pos / neg

the conjecture holds either for all x, y, or only for \(x, y \ge 0\), or only for \(x, y \le 0\)
