Nuprl Lemma : copath-nil_wf
∀[A:𝕌']. ∀[B:A ⟶ Type]. ∀[w:coW(A;a.B[a])]. (() ∈ copath(a.B[a];w))
Proof
Definitions occuring in Statement :
copath-nil: (),
copath: copath(a.B[a];w),
coW: coW(A;a.B[a]),
uall: ∀[x:A]. B[x],
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
copath-nil: (),
copath: copath(a.B[a];w),
nat: ℕ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
subtype_rel: A ⊆r B,
unit: Unit,
coPath: coPath(a.B[a];w;n),
eq_int: (i =z j),
subtract: n - m,
ifthenelse: if b then t else f fi ,
btrue: tt,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
decidable__le,
full-omega-unsat,
intformnot_wf,
intformle_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-le,
it_wf,
coPath_wf,
coW_wf,
istype-universe
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
Error :dependent_pairEquality_alt,
Error :dependent_set_memberEquality_alt,
natural_numberEquality,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesis,
unionElimination,
isectElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
Error :lambdaEquality_alt,
Error :isect_memberEquality_alt,
voidElimination,
Error :universeIsType,
hypothesisEquality,
applyEquality,
voidEquality,
Error :equalityIstype,
baseClosed,
because_Cache,
sqequalBase,
equalitySymmetry,
axiomEquality,
equalityTransitivity,
instantiate,
cumulativity,
Error :isectIsTypeImplies,
Error :inhabitedIsType,
Error :functionIsType,
universeEquality
Latex:
\mforall{}[A:\mBbbU{}']. \mforall{}[B:A {}\mrightarrow{} Type]. \mforall{}[w:coW(A;a.B[a])]. (() \mmember{} copath(a.B[a];w))
Date html generated:
2019_06_20-PM-00_56_36
Last ObjectModification:
2019_01_16-PM-02_57_10
Theory : co-recursion-2
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