Nuprl Lemma : predicate-shift_wf
∀[T:Type]. ∀[X:𝕌']. ∀[A:n:ℕ ⟶ (ℕn ⟶ T) ⟶ X]. ∀[x:T]. (A_x ∈ n:ℕ ⟶ (ℕn ⟶ T) ⟶ X)
Proof
Definitions occuring in Statement :
predicate-shift: A_x,
int_seg: {i..j-},
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
function: x:A ⟶ B[x],
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
predicate-shift: A_x,
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,
le: A ≤ B,
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
nat_wf,
int_seg_subtype,
int_seg_wf,
subtype_rel_dep_function,
seq-single_wf,
false_wf,
seq-append_wf,
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
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lambdaEquality,
applyEquality,
hypothesisEquality,
dependent_set_memberEquality,
addEquality,
sqequalHypSubstitution,
setElimination,
thin,
rename,
natural_numberEquality,
lemma_by_obid,
isectElimination,
hypothesis,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
cumulativity,
lambdaFormation,
because_Cache,
functionEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[T:Type]. \mforall{}[X:\mBbbU{}']. \mforall{}[A:n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} X]. \mforall{}[x:T]. (A\_x \mmember{} n:\mBbbN{} {}\mrightarrow{} (\mBbbN{}n {}\mrightarrow{} T) {}\mrightarrow{} X)
Date html generated:
2016_05_14-PM-04_07_10
Last ObjectModification:
2016_01_14-PM-10_58_11
Theory : fan-theorem
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