Nuprl Lemma : has-no-path_wf
∀[A:(𝔹 List) ⟶ ℙ]. (has-no-path(A) ∈ ℙ)
Proof
Definitions occuring in Statement :
has-no-path: has-no-path(A),
list: T List,
bool: 𝔹,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T,
function: x:A ⟶ B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
has-no-path: has-no-path(A),
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,
bool_wf,
exists_wf,
not_wf,
map_wf,
int_seg_wf,
subtype_rel_dep_function,
int_seg_subtype_nat,
false_wf,
subtype_rel_self,
upto_wf,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
functionEquality,
hypothesis,
lambdaEquality,
because_Cache,
applyEquality,
hypothesisEquality,
natural_numberEquality,
setElimination,
rename,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
cumulativity,
universeEquality
Latex:
\mforall{}[A:(\mBbbB{} List) {}\mrightarrow{} \mBbbP{}]. (has-no-path(A) \mmember{} \mBbbP{})
Date html generated:
2016_05_14-PM-04_12_32
Last ObjectModification:
2015_12_26-PM-07_54_05
Theory : fan-theorem
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