Nuprl Lemma : equiv-props_wf
∀[L:ℙ List]. (equiv-props(L) ∈ ℙ)
Proof
Definitions occuring in Statement :
equiv-props: equiv-props(L),
list: T List,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
equiv-props: equiv-props(L),
prop: ℙ,
so_lambda: λ2x.t[x],
int_seg: {i..j-},
uimplies: b supposing a,
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
not: ¬A,
implies: P ⇒ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
so_apply: x[s]
Lemmas referenced :
all_wf,
int_seg_wf,
length_wf,
iff_wf,
select_wf,
int_seg_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
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,
int_formula_prop_less_lemma,
list_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
closedConclusion,
natural_numberEquality,
instantiate,
universeEquality,
hypothesisEquality,
hypothesis,
Error :lambdaEquality_alt,
because_Cache,
setElimination,
rename,
independent_isectElimination,
productElimination,
imageElimination,
dependent_functionElimination,
unionElimination,
approximateComputation,
independent_functionElimination,
Error :dependent_pairFormation_alt,
int_eqEquality,
Error :isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
Error :universeIsType,
Error :inhabitedIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[L:\mBbbP{} List]. (equiv-props(L) \mmember{} \mBbbP{})
Date html generated:
2019_06_20-PM-01_50_10
Last ObjectModification:
2019_03_26-AM-10_21_04
Theory : list_1
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