Nuprl Lemma : sq_stable__rless-or3
∀x,y,a,b,c,d:ℝ. SqStable(((x < y) ∨ (a < b)) ∨ (c < d))
Proof
Definitions occuring in Statement :
rless: x < y,
real: ℝ,
sq_stable: SqStable(P),
all: ∀x:A. B[x],
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
sq_stable: SqStable(P),
implies: P ⇒ Q,
member: t ∈ T,
uall: ∀[x:A]. B[x],
prop: ℙ,
or: P ∨ Q,
squash: ↓T,
nat_plus: ℕ+,
decidable: Dec(P),
uimplies: b supposing a,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top,
false: False,
real: ℝ,
int_upper: {i...},
and: P ∧ Q,
iff: P ⇐⇒ Q,
subtype_rel: A ⊆r B,
so_lambda: λ2x.t[x],
so_apply: x[s],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
bfalse: ff,
sq_type: SQType(T),
guard: {T},
bnot: ¬bb,
ifthenelse: if b then t else f fi ,
assert: ↑b,
rev_implies: P ⇐ Q,
less_than: a < b,
bor: p ∨bq,
true: True,
has-value: (a)↓,
rless: x < y,
sq_exists: ∃x:A [B[x]]
Lemmas referenced :
squash_wf,
rless_wf,
real_wf,
quick-find_wf,
decidable__lt,
full-omega-unsat,
intformnot_wf,
intformless_wf,
itermConstant_wf,
istype-int,
int_formula_prop_not_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
istype-less_than,
bor_wf,
lt_int_wf,
int_upper_properties,
intformand_wf,
itermVar_wf,
intformle_wf,
int_formula_prop_and_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
istype-int_upper,
rless-iff4,
subtype_rel_sets_simple,
less_than_wf,
le_wf,
decidable__le,
nat_plus_properties,
eqtt_to_assert,
assert_of_lt_int,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_wf,
bool_subtype_base,
assert-bnot,
iff_weakening_uiff,
assert_wf,
add-is-int-iff,
itermAdd_wf,
int_term_value_add_lemma,
false_wf,
istype-assert,
iff_transitivity,
btrue_wf,
true_wf,
assert_of_bor,
or_functionality_wrt_uiff2,
istype-true,
or_functionality_wrt_iff,
iff_weakening_equal,
value-type-has-value,
int_upper_wf,
set-value-type,
int-value-type,
bfalse_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation_alt,
introduction,
universeIsType,
cut,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
sqequalRule,
unionEquality,
hypothesisEquality,
hypothesis,
inhabitedIsType,
imageElimination,
dependent_set_memberEquality_alt,
natural_numberEquality,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
approximateComputation,
independent_functionElimination,
dependent_pairFormation_alt,
lambdaEquality_alt,
isect_memberEquality_alt,
voidElimination,
addEquality,
applyEquality,
setElimination,
rename,
int_eqEquality,
independent_pairFormation,
because_Cache,
equalityIstype,
equalityTransitivity,
equalitySymmetry,
productElimination,
intEquality,
equalityElimination,
promote_hyp,
instantiate,
cumulativity,
pointwiseFunctionality,
baseApply,
closedConclusion,
baseClosed,
functionIsType,
inlFormation_alt,
unionIsType,
inrFormation_alt,
callbyvalueReduce,
inrEquality_alt,
inlEquality_alt
Latex:
\mforall{}x,y,a,b,c,d:\mBbbR{}. SqStable(((x < y) \mvee{} (a < b)) \mvee{} (c < d))
Date html generated:
2019_10_29-AM-09_35_11
Last ObjectModification:
2019_05_24-PM-00_19_59
Theory : reals
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