Nuprl Lemma : tree_leaf-value_wf
∀[E:Type]. ∀[v:tree(E)]. tree_leaf-value(v) ∈ E supposing ↑tree_leaf?(v)
Proof
Definitions occuring in Statement :
tree_leaf-value: tree_leaf-value(v),
tree_leaf?: tree_leaf?(v),
tree: tree(E),
assert: ↑b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
sq_type: SQType(T),
guard: {T},
eq_atom: x =a y,
ifthenelse: if b then t else f fi ,
tree_leaf?: tree_leaf?(v),
pi1: fst(t),
assert: ↑b,
tree_leaf-value: tree_leaf-value(v),
pi2: snd(t),
bfalse: ff,
exists: ∃x:A. B[x],
prop: ℙ,
or: P ∨ Q,
bnot: ¬bb,
false: False
Lemmas referenced :
tree-ext,
eq_atom_wf,
bool_wf,
eqtt_to_assert,
assert_of_eq_atom,
subtype_base_sq,
atom_subtype_base,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
bool_subtype_base,
assert-bnot,
neg_assert_of_eq_atom,
assert_wf,
tree_leaf?_wf,
tree_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
promote_hyp,
productElimination,
hypothesis_subsumption,
hypothesis,
applyEquality,
sqequalRule,
tokenEquality,
lambdaFormation,
unionElimination,
equalityElimination,
equalityTransitivity,
equalitySymmetry,
independent_isectElimination,
instantiate,
cumulativity,
atomEquality,
dependent_functionElimination,
independent_functionElimination,
because_Cache,
dependent_pairFormation,
voidElimination,
universeEquality
Latex:
\mforall{}[E:Type]. \mforall{}[v:tree(E)]. tree\_leaf-value(v) \mmember{} E supposing \muparrow{}tree\_leaf?(v)
Date html generated:
2017_10_01-AM-08_30_29
Last ObjectModification:
2017_07_26-PM-04_24_35
Theory : tree_1
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