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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