Nuprl Lemma : fset-size_wf
∀[T:Type]. ∀[eq:EqDecider(T)]. ∀[s:fset(T)]. (||s|| ∈ ℕ)
Proof
Definitions occuring in Statement :
fset-size: ||s||,
fset: fset(T),
deq: EqDecider(T),
nat: ℕ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
fset: fset(T),
quotient: x,y:A//B[x; y],
and: P ∧ Q,
fset-size: ||s||,
prop: ℙ,
nat: ℕ,
ge: i ≥ j ,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
set-equal: set-equal(T;x;y),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf,
l_member_wf,
member-remove-repeats,
remove-repeats-no_repeats,
set-equal-no_repeats-length,
le_wf,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
remove-repeats_wf,
non_neg_length,
deq_wf,
fset_wf,
set-equal_wf,
list_wf,
equal-wf-base,
nat_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
pointwiseFunctionalityForEquality,
lemma_by_obid,
hypothesis,
sqequalRule,
pertypeElimination,
productElimination,
thin,
productEquality,
isectElimination,
hypothesisEquality,
because_Cache,
cumulativity,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
universeEquality,
dependent_set_memberEquality,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
lambdaFormation,
addLevel,
impliesFunctionality,
independent_functionElimination
Latex:
\mforall{}[T:Type]. \mforall{}[eq:EqDecider(T)]. \mforall{}[s:fset(T)]. (||s|| \mmember{} \mBbbN{})
Date html generated:
2016_05_14-PM-03_45_39
Last ObjectModification:
2016_01_14-PM-10_39_41
Theory : finite!sets
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