Nuprl Lemma : int-rsub_wf
∀[k:ℤ]. ∀[x:ℝ]. (k - x ∈ ℝ)
Proof
Definitions occuring in Statement :
int-rsub: k - x,
real: ℝ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
int-rsub: k - x,
real: ℝ,
nat_plus: ℕ+,
prop: ℙ,
regular-int-seq: k-regular-seq(f),
all: ∀x:A. B[x],
top: Top,
squash: ↓T,
true: True,
subtype_rel: A ⊆r B,
uimplies: b supposing a,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
subtract: n - m
Lemmas referenced :
subtract_wf,
nat_plus_wf,
regular-int-seq_wf,
real_wf,
istype-int,
istype-void,
le_wf,
squash_wf,
true_wf,
absval_sym,
subtype_rel_self,
iff_weakening_equal,
minus-add,
minus-one-mul,
mul-associates,
one-mul,
mul-distributes,
add-associates,
mul-swap,
mul-commutes,
add-swap,
mul-distributes-right,
add-commutes,
zero-mul,
zero-add
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality_alt,
lambdaEquality_alt,
extract_by_obid,
isectElimination,
multiplyEquality,
natural_numberEquality,
hypothesisEquality,
hypothesis,
applyEquality,
universeIsType,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality_alt,
isectIsTypeImplies,
inhabitedIsType,
lambdaFormation_alt,
dependent_functionElimination,
because_Cache,
voidElimination,
minusEquality,
addEquality,
imageElimination,
imageMemberEquality,
baseClosed,
instantiate,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination
Latex:
\mforall{}[k:\mBbbZ{}]. \mforall{}[x:\mBbbR{}]. (k - x \mmember{} \mBbbR{})
Date html generated:
2019_10_29-AM-09_32_00
Last ObjectModification:
2019_02_13-PM-01_06_19
Theory : reals
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