Nuprl Lemma : Q-R-glued-conditional
∀[Info:Type]
∀es:EO+(Info)
∀[Q1,Q2,R:E ─→ E ─→ ℙ]. ∀[A,B:Type].
∀Ia1,Ia2:EClass(A). ∀Ib1,Ib2:EClass(B). ∀f:E([Ia1?Ia2]) ─→ B.
(Ia1:Q1 →─f─→ Ib1:R ⇒ Ia2:Q2 →─f─→ Ib2:R ⇒ [Ia1?Ia2]:Q1|{Ia1} ∨ Q2|{Ia2} →─f─→ [Ib1?Ib2]:R) supposing
(Ib1 ∩ Ib2 = 0 and
Ia1 ∩ Ia2 = 0)
Proof
Definitions occuring in Statement :
Q-R-glued: Ia:Qa →─f─→ Ib:Rb,
es-interface-disjoint: X ∩ Y = 0,
es-E-interface: E(X),
es-interface-predicate: {I},
cond-class: [X?Y],
eclass: EClass(A[eo; e]),
event-ordering+: EO+(Info),
es-E: E,
rel-restriction: R|P,
rel_or: R1 ∨ R2,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
function: x:A ─→ B[x],
universe: Type
Lemmas :
assert_wf,
in-eclass_wf,
es-E_wf,
event-ordering+_subtype,
es-interface-subtype_rel2,
cond-class_wf,
es-E-interface-conditional-subtype1,
es-E-interface_wf,
Q-R-glues-property,
subtype_rel_dep_function,
es-E-interface-conditional-subtype2,
Q-R-glued_wf,
es-interface-disjoint_wf,
top_wf,
eclass_wf,
event-ordering+_wf,
conditional_wf-interface2,
Q-R-glues_wf,
rel_or_wf,
rel-restriction_wf,
es-interface-predicate_wf,
Q-R-glues-conditional
Latex:
\mforall{}[Info:Type]
\mforall{}es:EO+(Info)
\mforall{}[Q1,Q2,R:E {}\mrightarrow{} E {}\mrightarrow{} \mBbbP{}]. \mforall{}[A,B:Type].
\mforall{}Ia1,Ia2:EClass(A). \mforall{}Ib1,Ib2:EClass(B). \mforall{}f:E([Ia1?Ia2]) {}\mrightarrow{} B.
(Ia1:Q1 \mrightarrow{}{}f{}\mrightarrow{} Ib1:R
{}\mRightarrow{} Ia2:Q2 \mrightarrow{}{}f{}\mrightarrow{} Ib2:R
{}\mRightarrow{} [Ia1?Ia2]:Q1|\{Ia1\} \mvee{} Q2|\{Ia2\} \mrightarrow{}{}f{}\mrightarrow{} [Ib1?Ib2]:R) supposing
(Ib1 \mcap{} Ib2 = 0 and
Ia1 \mcap{} Ia2 = 0)
Date html generated:
2015_07_21-PM-04_13_00
Last ObjectModification:
2015_01_27-PM-05_41_10
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