Theorem mulscan1d

Description: Cancellation of surreal multiplication when the left term is non-zero. (Contributed by Scott Fenton, 10-Mar-2025)

	Ref	Expression
Hypotheses	mulscan2d.1	$$⊢\phi \to A\in \mathrm{No}$$
	mulscan2d.2	$$⊢\phi \to B\in \mathrm{No}$$
	mulscan2d.3	$$⊢\phi \to C\in \mathrm{No}$$
	mulscan2d.4	No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
Assertion	mulscan1d	Could not format assertion : No typesetting found for |- ( ph -> ( ( C x.s A ) = ( C x.s B ) <-> A = B ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		mulscan2d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		mulscan2d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		mulscan2d.3	$$⊢\phi \to C\in \mathrm{No}$$
4		mulscan2d.4	Could not format ( ph -> C =/= 0s ) : No typesetting found for |- ( ph -> C =/= 0s ) with typecode |-
5	1 3	mulscomd	Could not format ( ph -> ( A x.s C ) = ( C x.s A ) ) : No typesetting found for |- ( ph -> ( A x.s C ) = ( C x.s A ) ) with typecode |-
6	2 3	mulscomd	Could not format ( ph -> ( B x.s C ) = ( C x.s B ) ) : No typesetting found for |- ( ph -> ( B x.s C ) = ( C x.s B ) ) with typecode |-
7	5 6	eqeq12d	Could not format ( ph -> ( ( A x.s C ) = ( B x.s C ) <-> ( C x.s A ) = ( C x.s B ) ) ) : No typesetting found for |- ( ph -> ( ( A x.s C ) = ( B x.s C ) <-> ( C x.s A ) = ( C x.s B ) ) ) with typecode |-
8	1 2 3 4	mulscan2d	Could not format ( ph -> ( ( A x.s C ) = ( B x.s C ) <-> A = B ) ) : No typesetting found for |- ( ph -> ( ( A x.s C ) = ( B x.s C ) <-> A = B ) ) with typecode |-
9	7 8	bitr3d	Could not format ( ph -> ( ( C x.s A ) = ( C x.s B ) <-> A = B ) ) : No typesetting found for |- ( ph -> ( ( C x.s A ) = ( C x.s B ) <-> A = B ) ) with typecode |-