Nuprl Lemma : CCC-bool
CCC(𝔹)
Proof
Definitions occuring in Statement :
contra-cc: CCC(T),
bool: 𝔹
Definitions unfolded in proof :
cand: A c∧ B,
true: True,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
ifthenelse: if b then t else f fi ,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
rev_implies: P ⇐ Q,
iff: P ⇐⇒ Q,
less_than': less_than'(a;b),
pi1: fst(t),
so_lambda: λ2x y.t[x; y],
nat: ℕ,
int_seg: {i..j-},
lelt: i ≤ j < k,
and: P ∧ Q,
le: A ≤ B,
less_than: a < b,
squash: ↓T,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
top: Top,
so_apply: x[s1;s2],
contra-cc: CCC(T),
all: ∀x:A. B[x],
implies: P ⇒ Q,
member: t ∈ T,
exists: ∃x:A. B[x],
subtype_rel: A ⊆r B,
prop: ℙ,
uall: ∀[x:A]. B[x]
Lemmas referenced :
istype-assert,
bool_cases,
iff_transitivity,
assert_of_bnot,
bnot_wf,
btrue_neq_bfalse,
int_term_value_subtract_lemma,
int_formula_prop_eq_lemma,
itermSubtract_wf,
intformeq_wf,
subtract_wf,
ge_wf,
subtract-1-ge-0,
btrue_wf,
iff_imp_equal_bool,
istype-true,
equal-wf-base,
set_subtype_base,
lelt_wf,
int_subtype_base,
not_wf,
equal_wf,
decidable__and2,
decidable__equal_int,
decidable__not,
decidable__equal_bool,
decidable-exists-finite,
decidable-all-finite,
finite-function,
nsub_finite,
finite-bool,
lt_int_wf,
eqtt_to_assert,
assert_of_lt_int,
bfalse_wf,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
less_than_wf,
int_seg_subtype_nat,
istype-false,
general-fan-theorem-troelstra2,
int_seg_wf,
int_seg_properties,
nat_properties,
decidable__le,
full-omega-unsat,
intformand_wf,
intformnot_wf,
intformle_wf,
itermConstant_wf,
itermVar_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_not_lemma,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_wf,
istype-le,
itermAdd_wf,
int_term_value_add_lemma,
decidable__lt,
intformless_wf,
int_formula_prop_less_lemma,
istype-less_than,
istype-nat,
bool_wf,
subtype_rel_self
Rules used in proof :
baseApply,
closedConclusion,
intWeakElimination,
functionIsTypeImplies,
baseClosed,
applyLambdaEquality,
intEquality,
sqequalBase,
inhabitedIsType,
equalityElimination,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
promote_hyp,
cumulativity,
functionExtensionality,
functionEquality,
dependent_functionElimination,
lambdaEquality_alt,
productEquality,
natural_numberEquality,
setElimination,
rename,
dependent_set_memberEquality_alt,
productElimination,
imageElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
addEquality,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
cut,
sqequalRule,
functionIsType,
introduction,
extract_by_obid,
hypothesis,
universeIsType,
productIsType,
because_Cache,
applyEquality,
hypothesisEquality,
thin,
instantiate,
sqequalHypSubstitution,
isectElimination,
universeEquality
Latex:
CCC(\mBbbB{})
Date html generated:
2019_10_15-AM-10_27_55
Last ObjectModification:
2019_08_26-PM-04_00_56
Theory : continuity
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