Theorem sltmuldivwd

Description: Surreal less-than relationship between division and multiplication. Weak version. (Contributed by Scott Fenton, 14-Mar-2025)

	Ref	Expression
Hypotheses	sltdivmulwd.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltdivmulwd.2	$$⊢\phi \to B\in \mathrm{No}$$
	sltdivmulwd.3	$$⊢\phi \to C\in \mathrm{No}$$
	sltdivmulwd.4	No typesetting found for |- ( ph -> 0s
	sltdivmulwd.5	No typesetting found for |- ( ph -> E. x e. No ( C x.s x ) = 1s ) with typecode |-
Assertion	sltmuldivwd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A x.s C ) A

Proof

Step	Hyp	Ref	Expression
1		sltdivmulwd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltdivmulwd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		sltdivmulwd.3	$$⊢\phi \to C\in \mathrm{No}$$
4		sltdivmulwd.4	Could not format ( ph -> 0s 0s
5		sltdivmulwd.5	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	4	sgt0ne0d	Could not format ( ph -> C =/= 0s ) : No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
7	2 3 6 5	divsclwd	Could not format ( ph -> ( B /su C ) e. No ) : No typesetting found for |- ( ph -> ( B /su C ) e. No ) with typecode |-
8	1 7 3 4	sltmul1d	Could not format ( ph -> ( A ( A x.s C ) ( A ( A x.s C )
9	2 3 6 5	divscan1wd	Could not format ( ph -> ( ( B /su C ) x.s C ) = B ) : No typesetting found for |- ( ph -> ( ( B /su C ) x.s C ) = B ) with typecode |-
10	9	breq2d	Could not format ( ph -> ( ( A x.s C ) ( A x.s C ) ( ( A x.s C ) ( A x.s C )
11	8 10	bitr2d	Could not format ( ph -> ( ( A x.s C ) A ( ( A x.s C ) A