Theorem divscan1wd

Description: A weak cancellation law for surreal division. (Contributed by Scott Fenton, 13-Mar-2025)

	Ref	Expression
Hypotheses	divscan2wd.1	$$⊢\phi \to A\in \mathrm{No}$$
	divscan2wd.2	$$⊢\phi \to B\in \mathrm{No}$$
	divscan2wd.3	No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
	divscan2wd.4	No typesetting found for |- ( ph -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
Assertion	divscan1wd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A /su B ) x.s B ) = A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		divscan2wd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		divscan2wd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		divscan2wd.3	Could not format ( ph -> B =/= 0s ) : No typesetting found for |- ( ph -> B =/= 0s ) with typecode |-
4		divscan2wd.4	Could not format ( ph -> E. x e. No ( B x.s x ) = 1s ) : No typesetting found for |- ( ph -> E. x e. No ( B x.s x ) = 1s ) with typecode |-
5	1 2 3 4	divsclwd	Could not format ( ph -> ( A /su B ) e. No ) : No typesetting found for |- ( ph -> ( A /su B ) e. No ) with typecode |-
6	5 2	mulscomd	Could not format ( ph -> ( ( A /su B ) x.s B ) = ( B x.s ( A /su B ) ) ) : No typesetting found for |- ( ph -> ( ( A /su B ) x.s B ) = ( B x.s ( A /su B ) ) ) with typecode |-
7	1 2 3 4	divscan2wd	Could not format ( ph -> ( B x.s ( A /su B ) ) = A ) : No typesetting found for |- ( ph -> ( B x.s ( A /su B ) ) = A ) with typecode |-
8	6 7	eqtrd	Could not format ( ph -> ( ( A /su B ) x.s B ) = A ) : No typesetting found for |- ( ph -> ( ( A /su B ) x.s B ) = A ) with typecode |-