Nuprl Lemma : prank_wf
∀[x:formula()]. (prank(x) ∈ ℕ)
Proof
Definitions occuring in Statement :
prank: prank(x),
formula: formula(),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
prank: prank(x),
so_lambda: λ2x.t[x],
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x y.t[x; y],
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
so_apply: x[s1;s2],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
guard: {T},
uiff: uiff(P;Q),
so_apply: x[s1;s2;s3;s4]
Lemmas referenced :
formula_ind_wf_simple,
nat_wf,
false_wf,
le_wf,
nat_properties,
decidable__le,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermAdd_wf,
itermVar_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
formula_wf,
imax_wf,
add_nat_wf,
imax_nat,
add-is-int-iff,
intformeq_wf,
int_formula_prop_eq_lemma,
equal_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
hypothesisEquality,
lambdaEquality,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
lambdaFormation,
atomEquality,
addEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
pointwiseFunctionality,
promote_hyp,
baseApply,
closedConclusion,
baseClosed,
productElimination,
independent_functionElimination,
axiomEquality
Latex:
\mforall{}[x:formula()]. (prank(x) \mmember{} \mBbbN{})
Date html generated:
2018_05_21-PM-08_52_36
Last ObjectModification:
2017_07_26-PM-06_15_50
Theory : general
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