Nuprl Lemma : altpath_wf
∀[T:Type]. ∀[A:n:ℕ ⟶ (ℕn ⟶ T) ⟶ 𝔹]. ∀[f:ℕ ⟶ T]. (IsPath(A;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
altpath: IsPath(A;f),
int_seg: {i..j-},
nat: ℕ,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
implies: P ⇒ Q,
not: ¬A,
false: False,
less_than': less_than'(a;b),
and: P ∧ Q,
le: A ≤ B,
uimplies: b supposing a,
nat: ℕ,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
prop: ℙ,
altpath: IsPath(A;f),
member: t ∈ T,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-universe,
bool_wf,
istype-nat,
subtype_rel_self,
istype-false,
int_seg_subtype_nat,
int_seg_wf,
subtype_rel_function,
assert_wf,
nat_wf
Rules used in proof :
universeEquality,
instantiate,
Error :inhabitedIsType,
Error :isectIsTypeImplies,
Error :isect_memberEquality_alt,
Error :universeIsType,
Error :functionIsType,
equalitySymmetry,
equalityTransitivity,
axiomEquality,
Error :lambdaFormation_alt,
independent_pairFormation,
independent_isectElimination,
because_Cache,
rename,
setElimination,
natural_numberEquality,
hypothesisEquality,
applyEquality,
thin,
isectElimination,
sqequalHypSubstitution,
hypothesis,
extract_by_obid,
functionEquality,
sqequalRule,
cut,
introduction,
Error :isect_memberFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}[T:Type]. \mforall{}[A:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} \mBbbB{}]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. (IsPath(A;f) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-02_46_23
Last ObjectModification:
2019_06_06-PM-01_46_26
Theory : fan-theorem
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