| Parents |
| hol |
| Children |
| surreal | gst-ax | wf_recp |
| Constants |
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trans
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('a 'a BOOL) BOOL
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tc
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('a 'a BOOL) 'a 'a BOOL
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|
well_founded
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('a 'a BOOL) BOOL
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|
twfp
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('a 'a BOOL) BOOL
|
| Definitions |
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trans
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r trans r ( s t u r s t r t u r s u)
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tc
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r tc r s t tr trans tr ( v u r v u tr v u) tr s t)
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well_founded
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r well_founded r ( s ( x ( y r y x s y) s x) ( x s x))
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twfp
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r twfp r well_founded r trans r
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| Theorems |
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tran_tc_thm
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r trans (tc r)
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tran_tc_thm2
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r x y z tc r x y tc r y z tc r x z
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tc_incr_thm
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r x y r x y tc r x y
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tc_decomp_thm
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r x y tc r x y r x y ( z tc r x z r z y)
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tc_mono_thm
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r1 r2 ( x y r1 x y r2 x y) ( x y tc r1 x y tc r2 x y)
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tc_p_thm
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r p ( x y r x y p x) ( x y tc r x y p x)
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tcwf_lemma1
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s r well_founded r ( x ( y tc r y x ( z tc r z y s z) s y) ( y tc r y x s y))
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tcwf_lemma2
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r well_founded r ( s ( t ( u tc r u t s u) s t) ( e s e))
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wf_tc_wf_thm
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r well_founded r well_founded (tc r)
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tc_wf_wf_thm
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r well_founded (tc r) well_founded r
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tc_wf_twf_thm
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r well_founded r twfp (tc r)
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wf_nochain_thm
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r
well_founded r ( x ( p v p v ( y p y tc r y x ( z p z r z y))))
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wf_wf_thm
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r well_founded r ( p v p v ( y p y ( z p z r z y)))
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nochain_wf_thm
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r
( x ( p v p v ( y p y tc r y x ( z p z r z y)))) well_founded r
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wf_induct_thm
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( p v p v ( y p y ( z p z r z y)))
well_founded r
|
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nochain_wf_thm2
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r
( x ( p v p v ( y p y ( z p z r z y)))) well_founded r
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nochain_min_thm
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r
( x ( p v p v ( y p y tc r y x ( z p z r z y)))) ( x ( y r y x) ( z r z x ( v r v z r v x)))
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|
nochain_min_thm2
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r
( x ( p v p v ( y p y ( z p z r z y)))) ( p ( y p y) ( z p z ( v r v z p v)))
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wf_min_thm
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r well_founded r ( x ( y r y x) ( z r z x ( v r v z r v x)))
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minr_not_wf_thm
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r
( x ( y r y x) ( z r z x ( v r v z r v x))) well_founded r
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wf_restrict_wf_thm
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r
well_founded r ( r2 well_founded ( x y r2 x y r x y))
|