Nuprl Lemma : Q-R-glues_functionality
∀[Info:Type]
∀es:EO+(Info)
∀[R:E ─→ E ─→ ℙ]. ∀[A,B:Type].
∀Ia:EClass(A). ∀Ib:EClass(B). ∀f:E(Ia) ─→ B.
∀[Q1,Q2:E ─→ E ─→ ℙ]. ∀g:E(Ib) ─→ E. (Q1 ⇐⇒ Q2 ⇒ (g glues Ia:Q1 ──f─→ Ib:R ⇐⇒ g glues Ia:Q2 ──f─→ Ib:R))
Proof
Definitions occuring in Statement :
Q-R-glues: g glues Ia:Qa ──f─→ Ib:Rb,
es-E-interface: E(X),
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
rel_equivalent: R1 ⇐⇒ R2,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
event-ordering+_subtype,
es-interface-predicate_wf,
interface_predicate_set_lemma,
es-E_wf,
exists_wf,
equal_wf,
es-E-interface-property,
es-interface-subtype_rel2,
event-ordering+_wf,
top_wf,
assert_wf,
in-eclass_wf,
subtype_rel_dep_function,
subtype_rel_self,
set_wf,
Q-R-pre-preserving_functionality_wrt_implies,
predicate_implies_weakening,
predicate_equivalent_weakening,
rel_implies_weakening,
rel_equivalent_inversion,
rel_equivalent_weakening,
es-E-interface_wf,
weak-antecedent-surjection-property
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B:Type].
\mforall{}Ia:EClass(A). \mforall{}Ib:EClass(B). \mforall{}f:E(Ia) {}\mrightarrow{} B.
\mforall{}[Q1,Q2:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}].
\mforall{}g:E(Ib) {}\mrightarrow{} E. (Q1 \mLeftarrow{}{}\mRightarrow{} Q2 {}\mRightarrow{} (g glues Ia:Q1 {}{}f{}\mrightarrow{} Ib:R \mLeftarrow{}{}\mRightarrow{} g glues Ia:Q2 {}{}f{}\mrightarrow{} Ib:R))
Date html generated:
2015_07_21-PM-04_08_22
Last ObjectModification:
2015_01_27-PM-06_05_25
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