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
Definitions unfolded in proof :
Q-R-pre-preserving: f is Q-R-pre-preserving on P,
guard: {T},
rel_implies: R1 => R2,
rel_rev_implies: R1 ⇐ R2,
predicate_rev_implies: P1 ⇐ P2,
infix_ap: x f y,
predicate_implies: P1 ⇒ P2,
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
exists: ∃x:A. B[x]
Latex:
\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:
2016_05_16-AM-10_18_40
Last ObjectModification:
2015_12_28-PM-09_25_16
Theory : new!event-ordering
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