Theorem posdifsd

Description: Comparison of two surreals whose difference is positive. (Contributed by Scott Fenton, 10-Mar-2025)

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

Proof

Step	Hyp	Ref	Expression
1		posdifsd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		posdifsd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		0sno	Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
4	3	a1i	Could not format ( ph -> 0s e. No ) : No typesetting found for |- ( ph -> 0s e. No ) with typecode |-
5	2 1	subscld	Could not format ( ph -> ( B -s A ) e. No ) : No typesetting found for |- ( ph -> ( B -s A ) e. No ) with typecode |-
6	4 5 1	sltadd1d	Could not format ( ph -> ( 0s ( 0s +s A ) ( 0s ( 0s +s A )
7		addslid	Could not format ( A e. No -> ( 0s +s A ) = A ) : No typesetting found for |- ( A e. No -> ( 0s +s A ) = A ) with typecode |-
8	1 7	syl	Could not format ( ph -> ( 0s +s A ) = A ) : No typesetting found for |- ( ph -> ( 0s +s A ) = A ) with typecode |-
9		npcans	Could not format ( ( B e. No /\ A e. No ) -> ( ( B -s A ) +s A ) = B ) : No typesetting found for |- ( ( B e. No /\ A e. No ) -> ( ( B -s A ) +s A ) = B ) with typecode |-
10	2 1 9	syl2anc	Could not format ( ph -> ( ( B -s A ) +s A ) = B ) : No typesetting found for |- ( ph -> ( ( B -s A ) +s A ) = B ) with typecode |-
11	8 10	breq12d	Could not format ( ph -> ( ( 0s +s A ) A ( ( 0s +s A ) A
12	6 11	bitr2d	Could not format ( ph -> ( A 0s ( A 0s