Nuprl Lemma : is-list-prop1
∀[t:Base]. t ∈ Base List supposing (is-list(t))↓
Proof
Definitions occuring in Statement :
is-list: is-list(t),
list: T List,
has-value: (a)↓,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
member: t ∈ T,
base: Base
Definitions unfolded in proof :
prop: ℙ,
member: t ∈ T,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
is-list: is-list(t),
nat: ℕ,
implies: P ⇒ Q,
false: False,
ge: i ≥ j ,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
and: P ∧ Q,
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
has-value: (a)↓,
subtype_rel: A ⊆r B,
pi2: snd(t),
cons: [a / b],
btrue: tt,
it: ⋅,
nil: []
Lemmas referenced :
base_wf,
has-value_wf_base,
nat_properties,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
istype-int,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
ge_wf,
istype-less_than,
fun_exp0_lemma,
strictness-apply,
bottom_diverge,
istype-universe,
istype-base,
subtract-1-ge-0,
fun_exp_unroll_1,
decidable__lt,
intformnot_wf,
int_formula_prop_not_lemma,
has-value-implies-dec-ispair,
int_subtype_base,
cons_wf,
has-value-implies-dec-isaxiom,
nil_wf
Rules used in proof :
hypothesisEquality,
baseClosed,
closedConclusion,
baseApply,
sqequalRule,
isectElimination,
extract_by_obid,
introduction,
instantiate,
thin,
hypothesis,
sqequalHypSubstitution,
cut,
isect_memberFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution,
compactness,
setElimination,
rename,
intWeakElimination,
lambdaFormation_alt,
natural_numberEquality,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
dependent_functionElimination,
Error :memTop,
independent_pairFormation,
universeIsType,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
functionIsTypeImplies,
inhabitedIsType,
because_Cache,
dependent_set_memberEquality_alt,
unionElimination,
callbyvalueCallbyvalue,
callbyvalueReduce,
applyEquality
Latex:
\mforall{}[t:Base]. t \mmember{} Base List supposing (is-list(t))\mdownarrow{}
Date html generated:
2020_05_20-AM-09_07_41
Last ObjectModification:
2020_01_17-AM-09_06_05
Theory : eval!all
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