Nuprl Lemma : bool-cmp_wf
bool-cmp() ∈ comparison(𝔹)
Proof
Definitions occuring in Statement :
bool-cmp: bool-cmp(),
comparison: comparison(T),
bool: 𝔹,
member: t ∈ T
Definitions unfolded in proof :
bool-cmp: bool-cmp(),
member: t ∈ T,
comparison: comparison(T),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
cand: A c∧ B,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
uimplies: b supposing a,
ifthenelse: if b then t else f fi ,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
prop: ℙ,
false: False,
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
assert: ↑b,
so_lambda: λ2x.t[x],
so_apply: x[s],
true: True,
le: A ≤ B,
less_than': less_than'(a;b),
not: ¬A
Lemmas referenced :
ifthenelse_wf,
bool_wf,
eqtt_to_assert,
decidable__equal_int,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
eqff_to_assert,
equal_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
equal-wf-T-base,
le_wf,
all_wf,
int_subtype_base,
false_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
dependent_set_memberEquality,
lambdaEquality,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
intEquality,
natural_numberEquality,
hypothesis,
minusEquality,
lambdaFormation,
unionElimination,
equalityElimination,
because_Cache,
productElimination,
independent_isectElimination,
dependent_functionElimination,
dependent_pairFormation,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
promote_hyp,
instantiate,
cumulativity,
equalityTransitivity,
equalitySymmetry,
independent_functionElimination,
independent_pairFormation,
baseClosed,
productEquality,
applyEquality,
functionExtensionality,
functionEquality,
addLevel,
levelHypothesis
Latex:
bool-cmp() \mmember{} comparison(\mBbbB{})
Date html generated:
2017_04_17-AM-08_26_48
Last ObjectModification:
2017_02_27-PM-04_48_29
Theory : list_1
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