Theorem npcans

Description: Cancellation law for surreal subtraction. (Contributed by Scott Fenton, 4-Feb-2025)

	Ref	Expression
Assertion	npcans	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( ( A -s B ) +s B ) = A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		subscl	Could not format ( ( A e. No /\ B e. No ) -> ( A -s B ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A -s B ) e. No ) with typecode |-
2		simpr	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to B\in \mathrm{No}$$
3	1 2	addscomd	Could not format ( ( A e. No /\ B e. No ) -> ( ( A -s B ) +s B ) = ( B +s ( A -s B ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( ( A -s B ) +s B ) = ( B +s ( A -s B ) ) ) with typecode |-
4		pncan3s	Could not format ( ( B e. No /\ A e. No ) -> ( B +s ( A -s B ) ) = A ) : No typesetting found for |- ( ( B e. No /\ A e. No ) -> ( B +s ( A -s B ) ) = A ) with typecode |-
5	4	ancoms	Could not format ( ( A e. No /\ B e. No ) -> ( B +s ( A -s B ) ) = A ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( B +s ( A -s B ) ) = A ) with typecode |-
6	3 5	eqtrd	Could not format ( ( A e. No /\ B e. No ) -> ( ( A -s B ) +s B ) = A ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( ( A -s B ) +s B ) = A ) with typecode |-