Nuprl Lemma : finite-unit
finite(Unit)
Proof
Definitions occuring in Statement :
finite: finite(T),
unit: Unit
Definitions unfolded in proof :
finite: finite(T),
exists: ∃x:A. B[x],
member: t ∈ T,
nat: ℕ,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
all: ∀x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
less_than: a < b,
squash: ↓T,
true: True
Lemmas referenced :
false_wf,
le_wf,
equipollent_wf,
unit_wf2,
int_seg_wf,
equipollent-unit,
int_seg_properties,
decidable__equal_int,
satisfiable-full-omega-tt,
intformand_wf,
intformnot_wf,
intformeq_wf,
itermVar_wf,
intformless_wf,
itermConstant_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
decidable__le,
decidable__lt,
lelt_wf,
equipollent_inversion
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
sqequalRule,
independent_pairFormation,
lambdaFormation,
hypothesis,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
setElimination,
rename,
independent_functionElimination,
independent_isectElimination,
productElimination,
dependent_functionElimination,
unionElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
because_Cache,
imageMemberEquality,
baseClosed
Latex:
finite(Unit)
Date html generated:
2016_10_21-AM-11_00_53
Last ObjectModification:
2016_08_07-PM-11_27_56
Theory : equipollence!!cardinality!
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