Nuprl Lemma : funtype-auto-test-case
∀m:ℕ. ∀A:ℕm ⟶ Type. ∀x:⋂x:Type. (x ⟶ x). ∀T:Type. (x ∈ funtype(0;A;T) ⟶ T)
Proof
Definitions occuring in Statement :
funtype: funtype(n;A;T),
int_seg: {i..j-},
nat: ℕ,
all: ∀x:A. B[x],
member: t ∈ T,
isect: ⋂x:A. B[x],
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
subtype_rel: A ⊆r B,
uall: ∀[x:A]. B[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s],
uimplies: b supposing a,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
funtype: funtype(n;A;T),
primrec: primrec(n;b;c)
Lemmas referenced :
funtype_wf,
false_wf,
le_wf,
subtype_rel_dep_function,
int_seg_wf,
int_seg_subtype,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
int_seg_properties,
intformless_wf,
int_formula_prop_less_lemma,
subtype_rel_self,
equal_wf,
nat_wf
Rules used in proof :
comment,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
hypothesisEquality,
applyEquality,
lambdaEquality,
isectElimination,
introduction,
extract_by_obid,
sqequalHypSubstitution,
thin,
cumulativity,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
hypothesis,
instantiate,
setElimination,
rename,
universeEquality,
because_Cache,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
productElimination,
equalityTransitivity,
equalitySymmetry,
functionEquality,
functionExtensionality,
independent_functionElimination,
isectEquality
Latex:
\mforall{}m:\mBbbN{}. \mforall{}A:\mBbbN{}m {}\mrightarrow{} Type. \mforall{}x:\mcap{}x:Type. (x {}\mrightarrow{} x). \mforall{}T:Type. (x \mmember{} funtype(0;A;T) {}\mrightarrow{} T)
Date html generated:
2017_10_01-AM-08_39_47
Last ObjectModification:
2017_07_26-PM-04_27_44
Theory : untyped!computation
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