Nuprl Lemma : mccarthy91-sqeq
∀x:Top. (mccarthy91(x) ~ if (x) < (102) then 91 else (x - 10))
Proof
Definitions occuring in Statement :
mccarthy91: mccarthy91(x),
top: Top,
all: ∀x:A. B[x],
less: if (a) < (b) then c else d,
subtract: n - m,
natural_number: $n,
sqequal: s ~ t
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
squash: ↓T,
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
less_than: a < b,
less_than': less_than'(a;b),
top: Top,
true: True,
not: ¬A,
false: False,
prop: ℙ,
bfalse: ff,
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
satisfiable_int_formula: satisfiable_int_formula(fmla),
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
subtype_rel: A ⊆r B,
mccarthy91: mccarthy91(x),
has-value: (a)↓
Lemmas referenced :
mccarthy91_wf1,
le_int_wf,
eqtt_to_assert,
assert_of_lt_int,
top_wf,
less_than_wf,
eqff_to_assert,
equal_wf,
bool_wf,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot,
full-omega-unsat,
intformand_wf,
intformle_wf,
itermVar_wf,
itermConstant_wf,
intformnot_wf,
intformless_wf,
int_formula_prop_and_lemma,
int_formula_prop_le_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_formula_prop_wf,
assert_wf,
bnot_wf,
not_wf,
le_wf,
bool_cases,
assert_of_le_int,
iff_transitivity,
iff_weakening_uiff,
assert_of_bnot,
sqle_wf_base,
squash_wf,
true_wf,
base_wf,
int_subtype_base,
subtype_rel_self,
iff_weakening_equal,
has-value_wf_base,
is-exception_wf,
exception-not-value,
value-type-has-value,
int-value-type
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
introduction,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
hypothesisEquality,
hypothesis,
intEquality,
isectElimination,
natural_numberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
applyLambdaEquality,
setElimination,
rename,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
unionElimination,
equalityElimination,
productElimination,
independent_isectElimination,
lessCases,
isect_memberFormation,
axiomSqEquality,
isect_memberEquality,
independent_pairFormation,
voidElimination,
voidEquality,
independent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity,
approximateComputation,
lambdaEquality,
int_eqEquality,
impliesFunctionality,
sqequalSqle,
sqleRule,
divergentSqle,
applyEquality,
baseApply,
closedConclusion,
universeEquality,
sqleReflexivity,
lessExceptionCases,
axiomSqleEquality,
exceptionSqequal,
callbyvalueLess
Latex:
\mforall{}x:Top. (mccarthy91(x) \msim{} if (x) < (102) then 91 else (x - 10))
Date html generated:
2019_06_20-PM-01_19_03
Last ObjectModification:
2018_08_20-PM-09_31_07
Theory : int_2
Home
Index