Theorem mulsfn

Description: Surreal multiplication is a function over surreals. (Contributed by Scott Fenton, 4-Feb-2025)

	Ref	Expression
Assertion	mulsfn	Could not format assertion : No typesetting found for |- x.s Fn ( No X. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		df-muls	Could not format x.s = norec2 ( ( z e. _V , m e. _V |-> [_ ( 1st ` z ) / x ]_ [_ ( 2nd ` z ) / y ]_ ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` y ) a = ( ( ( p m y ) +s ( x m q ) ) -s ( p m q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` y ) b = ( ( ( r m y ) +s ( x m s ) ) -s ( r m s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` y ) c = ( ( ( t m y ) +s ( x m u ) ) -s ( t m u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` y ) d = ( ( ( v m y ) +s ( x m w ) ) -s ( v m w ) ) } ) ) ) ) : No typesetting found for |- x.s = norec2 ( ( z e. _V , m e. _V |-> [_ ( 1st ` z ) / x ]_ [_ ( 2nd ` z ) / y ]_ ( ( { a | E. p e. ( _Left ` x ) E. q e. ( _Left ` y ) a = ( ( ( p m y ) +s ( x m q ) ) -s ( p m q ) ) } u. { b | E. r e. ( _Right ` x ) E. s e. ( _Right ` y ) b = ( ( ( r m y ) +s ( x m s ) ) -s ( r m s ) ) } ) |s ( { c | E. t e. ( _Left ` x ) E. u e. ( _Right ` y ) c = ( ( ( t m y ) +s ( x m u ) ) -s ( t m u ) ) } u. { d | E. v e. ( _Right ` x ) E. w e. ( _Left ` y ) d = ( ( ( v m y ) +s ( x m w ) ) -s ( v m w ) ) } ) ) ) ) with typecode |-
2	1	norec2fn	Could not format x.s Fn ( No X. No ) : No typesetting found for |- x.s Fn ( No X. No ) with typecode |-