Nuprl Lemma : coSet-bisimulation_wf
∀[R:coSet{i:l} ⟶ coSet{i:l} ⟶ ℙ']. (coSet-bisimulation{i:l}(x,y.R[x;y]) ∈ ℙ{i''})
Proof
Definitions occuring in Statement :
coSet-bisimulation: coSet-bisimulation{i:l}(x,y.R[x; y]),
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
coSet-bisimulation: coSet-bisimulation{i:l}(x,y.R[x; y]),
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q,
so_apply: x[s1;s2],
subtype_rel: A ⊆r B
Lemmas referenced :
coSet_wf,
subtype_rel_wf,
subtype_rel_self,
equal_wf,
subtype_coSet,
coSet_subtype
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
sqequalHypSubstitution,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsType,
universeIsType,
extract_by_obid,
inhabitedIsType,
hypothesisEquality,
universeEquality,
productEquality,
cumulativity,
thin,
instantiate,
isectElimination,
productElimination,
applyEquality,
because_Cache,
hypothesis_subsumption,
dependent_pairEquality_alt,
functionExtensionality
Latex:
\mforall{}[R:coSet\{i:l\} {}\mrightarrow{} coSet\{i:l\} {}\mrightarrow{} \mBbbP{}']. (coSet-bisimulation\{i:l\}(x,y.R[x;y]) \mmember{} \mBbbP{}\{i''\})
Date html generated:
2019_10_31-AM-06_32_46
Last ObjectModification:
2018_11_08-PM-05_58_47
Theory : constructive!set!theory
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