Nuprl Lemma : dep-all_wf
∀[n:ℕ]. ∀[P:nat-prop{i:l}(n)].  (dep-all(n;i.P[i]) ∈ ℙ)
Proof
Definitions occuring in Statement : 
dep-all: dep-all(n;i.P[i])
, 
nat-prop: nat-prop{i:l}(n)
, 
nat: ℕ
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
so_apply: x[s]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
and: P ∧ Q
, 
all: ∀x:A. B[x]
, 
nat: ℕ
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
uimplies: b supposing a
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
prop: ℙ
Lemmas referenced : 
nat-prop-dep-all-wf, 
decidable__lt, 
full-omega-unsat, 
intformnot_wf, 
intformless_wf, 
itermVar_wf, 
itermAdd_wf, 
itermConstant_wf, 
istype-int, 
int_formula_prop_not_lemma, 
int_formula_prop_less_lemma, 
int_term_value_var_lemma, 
int_term_value_add_lemma, 
int_term_value_constant_lemma, 
int_formula_prop_wf, 
istype-le, 
istype-less_than, 
istype-nat
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
productElimination, 
dependent_functionElimination, 
setElimination, 
rename, 
dependent_set_memberEquality_alt, 
independent_pairFormation, 
addEquality, 
natural_numberEquality, 
unionElimination, 
independent_isectElimination, 
approximateComputation, 
independent_functionElimination, 
dependent_pairFormation_alt, 
lambdaEquality_alt, 
int_eqEquality, 
Error :memTop, 
sqequalRule, 
universeIsType, 
voidElimination, 
productIsType, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry
Latex:
\mforall{}[n:\mBbbN{}].  \mforall{}[P:nat-prop\{i:l\}(n)].    (dep-all(n;i.P[i])  \mmember{}  \mBbbP{})
Date html generated:
2020_05_19-PM-09_39_53
Last ObjectModification:
2020_03_04-PM-03_46_58
Theory : co-recursion-2
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