Description: Square root theorem. Theorem I.35 of Apostol p. 29. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | sqrtthi.1 | |- A e. RR |
|
| Assertion | sqrtthi | |- ( 0 <_ A -> ( ( sqrt ` A ) x. ( sqrt ` A ) ) = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sqrtthi.1 | |- A e. RR |
|
| 2 | remsqsqrt | |- ( ( A e. RR /\ 0 <_ A ) -> ( ( sqrt ` A ) x. ( sqrt ` A ) ) = A ) |
|
| 3 | 1 2 | mpan | |- ( 0 <_ A -> ( ( sqrt ` A ) x. ( sqrt ` A ) ) = A ) |