Nuprl Lemma : Q-R-pre-preserving_wf
∀[es:EO]. ∀[P:E ⟶ ℙ]. ∀[Q,R:E ⟶ E ⟶ ℙ]. ∀[f:{e:E| P e} ⟶ E]. (f is Q-R-pre-preserving on P ∈ ℙ)
Proof
Definitions occuring in Statement :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
es-E: E,
event_ordering: EO,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
uall: ∀[x:A]. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
all: ∀x:A. B[x],
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s]
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]. (f is Q-R-pre-preserving on P \mmember{} \mBbbP{}\000C)
Date html generated:
2016_05_16-AM-10_18_31
Last ObjectModification:
2015_12_28-PM-09_22_46
Theory : new!event-ordering
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