Nuprl Lemma : cbva-intro-test3
∀x:ℤ. {y:ℤ| x * x < y}
Proof
Definitions occuring in Statement :
less_than: a < b,
all: ∀x:A. B[x],
set: {x:A| B[x]} ,
multiply: n * m,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
so_lambda: λ2x.t[x],
so_apply: x[s],
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
decidable: Dec(P),
or: P ∨ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
not: ¬A,
rev_implies: P ⇐ Q,
false: False,
uiff: uiff(P;Q),
subtract: n - m,
subtype_rel: A ⊆r B,
top: Top,
le: A ≤ B,
less_than': less_than'(a;b),
true: True,
prop: ℙ
Lemmas referenced :
int-valueall-type,
evalall-reduce,
set-value-type,
equal_wf,
valueall-type-value-type,
subtype_base_sq,
int_subtype_base,
decidable__lt,
istype-false,
not-lt-2,
condition-implies-le,
minus-add,
istype-void,
istype-int,
minus-one-mul,
add-swap,
minus-one-mul-top,
add-commutes,
add-mul-special,
zero-mul,
add-zero,
add-associates,
le-add-cancel,
less_than_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :lambdaFormation_alt,
cut,
introduction,
extract_by_obid,
hypothesis,
intEquality,
sqequalRule,
sqequalHypSubstitution,
isectElimination,
thin,
equalityTransitivity,
equalitySymmetry,
hypothesisEquality,
independent_isectElimination,
cutEval,
Error :dependent_set_memberEquality_alt,
Error :equalityIsType1,
Error :inhabitedIsType,
Error :lambdaEquality_alt,
Error :universeIsType,
setElimination,
rename,
because_Cache,
instantiate,
cumulativity,
dependent_functionElimination,
independent_functionElimination,
Error :dependent_set_memberFormation_alt,
addEquality,
multiplyEquality,
natural_numberEquality,
unionElimination,
independent_pairFormation,
voidElimination,
productElimination,
applyEquality,
Error :isect_memberEquality_alt,
minusEquality
Latex:
\mforall{}x:\mBbbZ{}. \{y:\mBbbZ{}| x * x < y\}
Date html generated:
2019_06_20-PM-01_05_06
Last ObjectModification:
2019_06_20-PM-00_59_52
Theory : fun_1
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