Nuprl Lemma : fix_wf_coSet_system_weak
∀[I:𝕌']. ∀[G:⋂C:𝕌'. ((I ⟶ C) ⟶ I ⟶ (T:Type × (T ⟶ C)))]. (fix(G) ∈ I ⟶ coSet{i:l})
Proof
Definitions occuring in Statement :
coSet: coSet{i:l},
uall: ∀[x:A]. B[x],
member: t ∈ T,
fix: fix(F),
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
product: x:A × B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prop: ℙ,
so_lambda: λ2x.t[x],
and: P ∧ Q,
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
fix_wf_coSet_system,
set_wf,
subtype_rel_wf,
coSet_wf
Rules used in proof :
cut,
introduction,
extract_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
isect_memberEquality,
setElimination,
rename,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
sqequalRule,
lambdaEquality,
productEquality,
functionEquality,
cumulativity,
applyEquality,
because_Cache,
isectEquality
Latex:
\mforall{}[I:\mBbbU{}']. \mforall{}[G:\mcap{}C:\mBbbU{}'. ((I {}\mrightarrow{} C) {}\mrightarrow{} I {}\mrightarrow{} (T:Type \mtimes{} (T {}\mrightarrow{} C)))]. (fix(G) \mmember{} I {}\mrightarrow{} coSet\{i:l\})
Date html generated:
2019_10_31-AM-06_33_00
Last ObjectModification:
2018_08_08-AM-08_17_01
Theory : constructive!set!theory
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