Nuprl Lemma : mccarthy91_wf
∀x:ℤ. (mccarthy91(x) ∈ {91...})
Proof
Definitions occuring in Statement :
mccarthy91: mccarthy91(x),
int_upper: {i...},
all: ∀x:A. B[x],
member: t ∈ T,
natural_number: $n,
int: ℤ
Definitions unfolded in proof :
top: Top,
satisfiable_int_formula: satisfiable_int_formula(fmla),
decidable: Dec(P),
sq_stable: SqStable(P),
not: ¬A,
false: False,
assert: ↑b,
bnot: ¬bb,
sq_type: SQType(T),
or: P ∨ Q,
exists: ∃x:A. B[x],
bfalse: ff,
guard: {T},
squash: ↓T,
prop: ℙ,
so_apply: x[s],
so_lambda: λ2x.t[x],
int_upper: {i...},
ifthenelse: if b then t else f fi ,
uimplies: b supposing a,
and: P ∧ Q,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
btrue: tt,
it: ⋅,
unit: Unit,
bool: 𝔹,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
member: t ∈ T,
all: ∀x:A. B[x]
Lemmas referenced :
int_term_value_subtract_lemma,
itermSubtract_wf,
int_formula_prop_wf,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
full-omega-unsat,
decidable__le,
assert-bnot,
bool_subtype_base,
subtype_base_sq,
bool_cases_sqequal,
equal_wf,
eqff_to_assert,
sq_stable__equal,
bool_wf,
le_int_wf,
le_wf,
int_subtype_base,
equal-wf-base,
subtype_rel_sets,
assert_of_le_int,
eqtt_to_assert,
mccarthy91_wf1
Rules used in proof :
closedConclusion,
baseApply,
independent_pairFormation,
voidEquality,
isect_memberEquality,
int_eqEquality,
approximateComputation,
voidElimination,
independent_functionElimination,
cumulativity,
instantiate,
promote_hyp,
dependent_pairFormation,
equalitySymmetry,
equalityTransitivity,
imageElimination,
imageMemberEquality,
applyLambdaEquality,
setEquality,
rename,
setElimination,
baseClosed,
lambdaEquality,
intEquality,
sqequalRule,
natural_numberEquality,
independent_isectElimination,
productElimination,
isectElimination,
equalityElimination,
unionElimination,
because_Cache,
applyEquality,
hypothesis,
hypothesisEquality,
thin,
dependent_functionElimination,
sqequalHypSubstitution,
extract_by_obid,
introduction,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}x:\mBbbZ{}. (mccarthy91(x) \mmember{} \{91...\})
Date html generated:
2018_05_21-PM-00_30_45
Last ObjectModification:
2017_12_27-PM-06_47_29
Theory : int_2
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