Nuprl Lemma : select_fun_last_wf
∀[m:ℕ]. ∀[A:ℕm + 1 ⟶ Type]. ∀[g:∀[T:Type]. (funtype(m + 1;A;T) ⟶ T)]. (select_fun_last(g;m) ∈ A m)
Proof
Definitions occuring in Statement :
select_fun_last: select_fun_last(g;m),
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
apply: f a,
function: x:A ⟶ B[x],
add: n + m,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
select_fun_last: select_fun_last(g;m),
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ,
int_seg: {i..j-},
lelt: i ≤ j < k,
le: A ≤ B,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
so_apply: x[s]
Lemmas referenced :
nat_wf,
int_seg_wf,
funtype_wf,
uall_wf,
lelt_wf,
int_formula_prop_less_lemma,
intformless_wf,
decidable__lt,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermAdd_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_properties,
select_fun_ap_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
hypothesisEquality,
natural_numberEquality,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
instantiate,
universeEquality,
functionEquality,
cumulativity,
applyEquality
Latex:
\mforall{}[m:\mBbbN{}]. \mforall{}[A:\mBbbN{}m + 1 {}\mrightarrow{} Type]. \mforall{}[g:\mforall{}[T:Type]. (funtype(m + 1;A;T) {}\mrightarrow{} T)].
(select\_fun\_last(g;m) \mmember{} A m)
Date html generated:
2016_05_15-PM-02_10_20
Last ObjectModification:
2016_01_15-PM-10_20_50
Theory : untyped!computation
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