Nuprl Lemma : is-path_wf
∀[T:Type]. ∀[A:(T List) ⟶ ℙ]. ∀[f:ℕ ⟶ T]. (is-path(A;f) ∈ ℙ)
Proof
Definitions occuring in Statement :
is-path: is-path(A;f),
list: T List,
nat: ℕ,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
is-path: is-path(A;f),
so_lambda: λ2x.t[x],
nat: ℕ,
subtype_rel: A ⊆r B,
so_apply: x[s],
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x]
Lemmas referenced :
all_wf,
nat_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
upto_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
applyEquality,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
cumulativity,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
because_Cache,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionEquality,
isect_memberEquality,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[A:(T List) {}\mrightarrow{} \mBbbP{}]. \mforall{}[f:\mBbbN{} {}\mrightarrow{} T]. (is-path(A;f) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_09_52
Last ObjectModification:
2015_12_26-PM-07_54_32
Theory : fan-theorem
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