Nuprl Lemma : Q-R-pre-preserving_functionality_wrt_implies
∀es:EO
∀[P1,P2:E ─→ ℙ]. ∀[Q1,R1,Q2,R2:E ─→ E ─→ ℙ].
∀f:{e:E| P1 e} ─→ E
(P1 ⇐ P2 ⇒ Q1 ⇐ Q2 ⇒ R1 => R2 ⇒ {f is Q1-R1-pre-preserving on P1 ⇒ f is Q2-R2-pre-preserving on P2})
Proof
Definitions occuring in Statement :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
es-E: E,
event_ordering: EO,
predicate_rev_implies: P1 ⇐ P2,
rel_rev_implies: R1 ⇐ R2,
rel_implies: R1 => R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
all: ∀x:A. B[x],
exists: ∃x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
apply: f a,
function: x:A ─→ B[x],
equal: s = t ∈ T
Lemmas :
subtype_rel_sets,
es-E_wf,
set_wf,
all_wf,
exists_wf,
equal_wf,
event_ordering_wf
\mforall{}es:EO
\mforall{}[P1,P2:E {}\mrightarrow{} \mBbbP{}]. \mforall{}[Q1,R1,Q2,R2:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}f:\{e:E| P1 e\} {}\mrightarrow{} E
(P1 \mLeftarrow{}{} P2
{}\mRightarrow{} Q1 \mLeftarrow{}{} Q2
{}\mRightarrow{} R1 => R2
{}\mRightarrow{} \{f is Q1-R1-pre-preserving on P1 {}\mRightarrow{} f is Q2-R2-pre-preserving on P2\})
Date html generated:
2015_07_17-AM-09_03_01
Last ObjectModification:
2015_01_27-PM-00_55_14
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