Theorem adds4d

Description: Rearrangement of four terms in a surreal sum. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	adds4d.1	$$⊢\phi \to A\in \mathrm{No}$$
	adds4d.2	$$⊢\phi \to B\in \mathrm{No}$$
	adds4d.3	$$⊢\phi \to C\in \mathrm{No}$$
	adds4d.4	$$⊢\phi \to D\in \mathrm{No}$$
Assertion	adds4d	Could not format assertion : No typesetting found for |- ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( B +s D ) ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		adds4d.1	$$⊢\phi \to A\in \mathrm{No}$$
2		adds4d.2	$$⊢\phi \to B\in \mathrm{No}$$
3		adds4d.3	$$⊢\phi \to C\in \mathrm{No}$$
4		adds4d.4	$$⊢\phi \to D\in \mathrm{No}$$
5	1 2 3	adds32d	Could not format ( ph -> ( ( A +s B ) +s C ) = ( ( A +s C ) +s B ) ) : No typesetting found for |- ( ph -> ( ( A +s B ) +s C ) = ( ( A +s C ) +s B ) ) with typecode |-
6	5	oveq1d	Could not format ( ph -> ( ( ( A +s B ) +s C ) +s D ) = ( ( ( A +s C ) +s B ) +s D ) ) : No typesetting found for |- ( ph -> ( ( ( A +s B ) +s C ) +s D ) = ( ( ( A +s C ) +s B ) +s D ) ) with typecode |-
7	1 2	addscld	Could not format ( ph -> ( A +s B ) e. No ) : No typesetting found for |- ( ph -> ( A +s B ) e. No ) with typecode |-
8	7 3 4	addsassd	Could not format ( ph -> ( ( ( A +s B ) +s C ) +s D ) = ( ( A +s B ) +s ( C +s D ) ) ) : No typesetting found for |- ( ph -> ( ( ( A +s B ) +s C ) +s D ) = ( ( A +s B ) +s ( C +s D ) ) ) with typecode |-
9	1 3	addscld	Could not format ( ph -> ( A +s C ) e. No ) : No typesetting found for |- ( ph -> ( A +s C ) e. No ) with typecode |-
10	9 2 4	addsassd	Could not format ( ph -> ( ( ( A +s C ) +s B ) +s D ) = ( ( A +s C ) +s ( B +s D ) ) ) : No typesetting found for |- ( ph -> ( ( ( A +s C ) +s B ) +s D ) = ( ( A +s C ) +s ( B +s D ) ) ) with typecode |-
11	6 8 10	3eqtr3d	Could not format ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( B +s D ) ) ) : No typesetting found for |- ( ph -> ( ( A +s B ) +s ( C +s D ) ) = ( ( A +s C ) +s ( B +s D ) ) ) with typecode |-