Nuprl Lemma : l_succ_wf
∀[T:Type]. ∀[l:T List]. ∀[x:T]. ∀[P:T ⟶ ℙ]. (y = succ(x) in l⇒ P[y] ∈ ℙ)
Proof
Definitions occuring in Statement :
l_succ: l_succ,
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s],
member: t ∈ T,
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
l_succ: l_succ,
so_lambda: λ2x.t[x],
implies: P ⇒ Q,
prop: ℙ,
nat: ℕ,
uimplies: b supposing a,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
and: P ∧ Q,
less_than: a < b,
squash: ↓T,
so_apply: x[s],
subtype_rel: A ⊆r B
Lemmas referenced :
all_wf,
nat_wf,
less_than_wf,
length_wf,
equal_wf,
select_wf,
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,
decidable__lt,
intformless_wf,
itermAdd_wf,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
functionEquality,
addEquality,
setElimination,
rename,
because_Cache,
natural_numberEquality,
cumulativity,
hypothesisEquality,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
imageElimination,
productElimination,
applyEquality,
functionExtensionality,
universeEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[T:Type]. \mforall{}[l:T List]. \mforall{}[x:T]. \mforall{}[P:T {}\mrightarrow{} \mBbbP{}]. (y = succ(x) in l{}\mRightarrow{} P[y] \mmember{} \mBbbP{})
Date html generated:
2017_10_01-AM-08_33_47
Last ObjectModification:
2017_07_26-PM-04_25_17
Theory : list!
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