Nuprl Lemma : Q-R-pre-preserving-1-1
∀[es:EO]. ∀[P:E ⟶ ℙ]. ∀[Q,R:E ⟶ E ⟶ ℙ]. ∀[f:{e:E| P e} ⟶ E].
(Inj({e:E| P e} ;E;f)) supposing (f is Q-R-pre-preserving on P and AntiSym(E;e,e'.R e e') and Refl(E;e,e'.Q e e'))
Proof
Definitions occuring in Statement :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
es-E: E,
event_ordering: EO,
anti_sym: AntiSym(T;x,y.R[x; y]),
refl: Refl(T;x,y.E[x; y]),
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
inject: Inj(A;B;f),
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
anti_sym: AntiSym(T;x,y.R[x; y]),
refl: Refl(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s],
and: P ∧ Q,
cand: A c∧ B,
guard: {T}
Latex:
\mforall{}[es:EO]. \mforall{}[P:E {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:\{e:E| P e\} {}\mrightarrow{} E].
(Inj(\{e:E| P e\} ;E;f)) supposing
(f is Q-R-pre-preserving on P and
AntiSym(E;e,e'.R e e') and
Refl(E;e,e'.Q e e'))
Date html generated:
2016_05_16-AM-10_19_11
Last ObjectModification:
2015_12_28-PM-09_23_18
Theory : new!event-ordering
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