Theorem divscan1d

Description: A cancellation law for surreal division. (Contributed by Scott Fenton, 16-Mar-2025)

	Ref	Expression
Hypotheses	divscan2d.1	|- ( ph -> A e. No )
	divscan2d.2	|- ( ph -> B e. No )
	divscan2d.3	|- ( ph -> B =/= 0s )
Assertion	divscan1d	|- ( ph -> ( ( A /su B ) x.s B ) = A )

Proof

Step	Hyp	Ref	Expression
1		divscan2d.1	|- ( ph -> A e. No )
2		divscan2d.2	|- ( ph -> B e. No )
3		divscan2d.3	|- ( ph -> B =/= 0s )
4	2 3	recsexd	|- ( ph -> E. x e. No ( B x.s x ) = 1s )
5	1 2 3 4	divscan1wd	|- ( ph -> ( ( A /su B ) x.s B ) = A )