Theorem sltmuldivd

Description: Surreal less-than relationship between division and multiplication. (Contributed by Scott Fenton, 16-Mar-2025)

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

Proof

Step	Hyp	Ref	Expression
1		sltdivmuld.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltdivmuld.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltdivmuld.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltdivmuld.4	Could not format ( ph -> 0s 0s
5	4	sgt0ne0d	Could not format ( ph -> C =/= 0s ) : No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
6	3 5	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 |-
7	1 2 3 4 6	sltmuldivwd	Could not format ( ph -> ( ( A x.s C ) A ( ( A x.s C ) A