Nuprl Lemma : awf-system-subtype
∀[I,A:Type]. (awf-system{i:l}(I;A) ⊆r ((I ⟶ awf(A)) ⟶ I ⟶ awf(A)))
Proof
Definitions occuring in Statement :
awf-system: awf-system{i:l}(I;A),
awf: awf(T),
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
all: ∀x:A. B[x],
implies: P ⇒ Q,
awf: awf(T),
guard: {T},
awf-system: awf-system{i:l}(I;A),
and: P ∧ Q,
or: P ∨ Q,
subtype_rel: A ⊆r B,
cand: A c∧ B,
prop: ℙ
Lemmas referenced :
corec-ext,
list_wf,
continuous-monotone-union,
continuous-monotone-constant,
continuous-monotone-list,
continuous-monotone-id,
ext-eq_inversion,
awf_wf,
subtype_rel_weakening,
isect2_subtype_rel3,
subtype_rel_wf,
top_wf,
subtype_rel_self,
subtype_rel_dep_function,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
lambdaEquality,
unionEquality,
cumulativity,
hypothesisEquality,
hypothesis,
universeEquality,
independent_isectElimination,
dependent_functionElimination,
independent_functionElimination,
instantiate,
isectEquality,
setEquality,
productEquality,
functionEquality,
setElimination,
rename,
inlFormation,
independent_pairFormation,
dependent_set_memberEquality,
equalityTransitivity,
equalitySymmetry,
lambdaFormation,
functionExtensionality,
applyEquality,
because_Cache,
axiomEquality,
isect_memberEquality
Latex:
\mforall{}[I,A:Type]. (awf-system\{i:l\}(I;A) \msubseteq{}r ((I {}\mrightarrow{} awf(A)) {}\mrightarrow{} I {}\mrightarrow{} awf(A)))
Date html generated:
2018_05_21-PM-08_56_31
Last ObjectModification:
2017_07_26-PM-06_20_17
Theory : general
Home
Index