Theorem divsmuld

Description: Relationship between surreal division and multiplication. (Contributed by Scott Fenton, 16-Mar-2025)

	Ref	Expression
Hypotheses	divsmuld.1	$$⊢\phi \to A\in \mathrm{No}$$
	divsmuld.2	$$⊢\phi \to B\in \mathrm{No}$$
	divsmuld.3	$$⊢\phi \to C\in \mathrm{No}$$
	divsmuld.4	No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
Assertion	divsmuld	Could not format assertion : No typesetting found for |- ( ph -> ( ( A /su C ) = B <-> ( C x.s B ) = A ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		divsmuld.1	$$⊢\phi \to A\in \mathrm{No}$$
2		divsmuld.2	$$⊢\phi \to B\in \mathrm{No}$$
3		divsmuld.3	$$⊢\phi \to C\in \mathrm{No}$$
4		divsmuld.4	Could not format ( ph -> C =/= 0s ) : No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
5	3 4	recsexd	Could not format ( ph -> E. x e. No ( C x.s x ) = 1s ) : No typesetting found for |- ( ph -> E. x e. No ( C x.s x ) = 1s ) with typecode |-
6	1 2 3 4 5	divsmulwd	Could not format ( ph -> ( ( A /su C ) = B <-> ( C x.s B ) = A ) ) : No typesetting found for |- ( ph -> ( ( A /su C ) = B <-> ( C x.s B ) = A ) ) with typecode |-