Nuprl Lemma : singleton-type-one
singleton-type(ℕ1)
Proof
Definitions occuring in Statement :
singleton-type: singleton-type(A),
int_seg: {i..j-},
natural_number: $n
Definitions unfolded in proof :
singleton-type: singleton-type(A),
exists: ∃x:A. B[x],
member: t ∈ T,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
less_than: a < b,
squash: ↓T,
true: True,
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
top: Top,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
equal_wf,
all_wf,
int_seg_wf,
decidable__lt,
decidable__le,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformle_wf,
intformless_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
int_seg_properties,
lelt_wf,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
dependent_pairFormation,
dependent_set_memberEquality,
natural_numberEquality,
independent_pairFormation,
sqequalRule,
lambdaFormation,
hypothesis,
cut,
lemma_by_obid,
introduction,
imageMemberEquality,
hypothesisEquality,
thin,
baseClosed,
sqequalHypSubstitution,
isectElimination,
setElimination,
rename,
productElimination,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
equalityTransitivity,
equalitySymmetry,
because_Cache
Latex:
singleton-type(\mBbbN{}1)
Date html generated:
2016_05_14-PM-04_02_14
Last ObjectModification:
2016_01_14-PM-11_05_56
Theory : equipollence!!cardinality!
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