Nuprl Lemma : monotone-incr-chain
∀F:Type ⟶ Type. (Monotone(T.F T) ⇒ (λn.(F^n Void) ∈ type-incr-chain{i:l}()))
Proof
Definitions occuring in Statement :
type-incr-chain: type-incr-chain{i:l}(),
type-monotone: Monotone(T.F[T]),
fun_exp: f^n,
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
apply: f a,
lambda: λx.A[x],
function: x:A ⟶ B[x],
void: Void,
universe: Type
Definitions unfolded in proof :
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
so_apply: x[s],
nat: ℕ,
ge: i ≥ j ,
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,
prop: ℙ,
type-incr-chain: type-incr-chain{i:l}(),
so_lambda: λ2x.t[x]
Lemmas referenced :
type-monotone_wf,
subtype_rel_wf,
all_wf,
fun_exp_wf,
nat_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,
type-monotone-fun_exp
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
independent_isectElimination,
hypothesis,
dependent_set_memberEquality,
addEquality,
setElimination,
rename,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
because_Cache,
applyEquality,
instantiate,
universeEquality,
functionEquality
Latex:
\mforall{}F:Type {}\mrightarrow{} Type. (Monotone(T.F T) {}\mRightarrow{} (\mlambda{}n.(F\^{}n Void) \mmember{} type-incr-chain\{i:l\}()))
Date html generated:
2016_05_15-PM-06_52_03
Last ObjectModification:
2016_01_16-AM-09_49_53
Theory : general
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