Proof

$$(x > -10) \to$$   True $$, (y \geq 0) \to (y \geq -5)$$

is True , so we use weakening:

$$\frac{(x > -10) \to \mbox{true}, (y \geq 0) \to (y \geq -5), \lan... ...0 \rangle }{\langle x > -10 \rangle \; y := x^2 \; \langle y \geq -5 \rangle }$$