Nuprl Lemma : not-d-CCC-nat
¬dCCC(ℕ)
Proof
Definitions occuring in Statement :
contra-dcc: dCCC(T),
nat: ℕ,
not: ¬A
Definitions unfolded in proof :
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
guard: {T},
bfalse: ff,
true: True,
btrue: tt,
ifthenelse: if b then t else f fi ,
assert: ↑b,
isl: isl(x),
so_apply: x[s],
so_lambda: λ2x.t[x],
less_than': less_than'(a;b),
subtype_rel: A ⊆r B,
top: Top,
false: False,
satisfiable_int_formula: satisfiable_int_formula(fmla),
uimplies: b supposing a,
or: P ∨ Q,
decidable: Dec(P),
ge: i ≥ j ,
squash: ↓T,
less_than: a < b,
le: A ≤ B,
and: P ∧ Q,
lelt: i ≤ j < k,
int_seg: {i..j-},
nat: ℕ,
exists: ∃x:A. B[x],
all: ∀x:A. B[x],
prop: ℙ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
contra-dcc: dCCC(T),
implies: P ⇒ Q,
not: ¬A
Lemmas referenced :
not-LPO,
iff_weakening_equal,
istype-universe,
true_wf,
squash_wf,
equal_wf,
int_term_value_add_lemma,
itermAdd_wf,
istype-true,
istype-less_than,
int_formula_prop_eq_lemma,
int_formula_prop_less_lemma,
intformeq_wf,
intformless_wf,
istype-assert,
bfalse_wf,
btrue_wf,
decidable_wf,
subtype_rel_self,
decidable__equal_int,
decidable__all_int_seg,
decidable__lt,
decidable__exists_int_seg,
int_subtype_base,
le_wf,
set_subtype_base,
istype-false,
int_seg_subtype_nat,
equal-wf-base,
istype-nat,
istype-le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_and_lemma,
istype-int,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
nat_properties,
int_seg_properties,
less_than_wf,
int_seg_wf,
decidable__or,
nat_wf,
contra-dcc_wf
Rules used in proof :
imageMemberEquality,
universeEquality,
addEquality,
Error :unionIsType,
Error :productIsType,
applyLambdaEquality,
Error :inrFormation_alt,
sqequalBase,
Error :functionIsType,
Error :inlFormation_alt,
equalitySymmetry,
equalityTransitivity,
Error :equalityIstype,
Error :inhabitedIsType,
unionEquality,
functionExtensionality,
because_Cache,
instantiate,
baseClosed,
intEquality,
functionEquality,
independent_pairFormation,
voidElimination,
Error :isect_memberEquality_alt,
int_eqEquality,
Error :lambdaEquality_alt,
Error :dependent_pairFormation_alt,
independent_functionElimination,
approximateComputation,
independent_isectElimination,
unionElimination,
dependent_functionElimination,
imageElimination,
Error :dependent_set_memberEquality_alt,
applyEquality,
productElimination,
hypothesisEquality,
rename,
setElimination,
natural_numberEquality,
productEquality,
sqequalRule,
hypothesis,
thin,
isectElimination,
extract_by_obid,
introduction,
cut,
Error :universeIsType,
sqequalHypSubstitution,
Error :lambdaFormation_alt,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mneg{}dCCC(\mBbbN{})
Date html generated:
2019_06_20-PM-03_00_31
Last ObjectModification:
2019_06_12-PM-08_24_12
Theory : continuity
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