Nuprl Lemma : radd_functionality
∀[a1,a2,b1,b2:ℝ]. ((a1 + b1) = (a2 + b2)) supposing ((a1 = a2) and (b1 = b2))
Proof
Definitions occuring in Statement :
req: x = y
,
radd: a + b
,
real: ℝ
,
uimplies: b supposing a
,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x]
,
member: t ∈ T
,
uimplies: b supposing a
,
squash: ↓T
,
prop: ℙ
,
true: True
,
subtype_rel: A ⊆r B
,
guard: {T}
,
iff: P
⇐⇒ Q
,
and: P ∧ Q
,
rev_implies: P
⇐ Q
,
implies: P
⇒ Q
,
cand: A c∧ B
,
length: ||as||
,
list_ind: list_ind,
cons: [a / b]
,
nil: []
,
it: ⋅
,
all: ∀x:A. B[x]
,
top: Top
,
int_seg: {i..j-}
,
decidable: Dec(P)
,
or: P ∨ Q
,
sq_type: SQType(T)
,
select: L[n]
,
le: A ≤ B
,
less_than': less_than'(a;b)
,
false: False
,
not: ¬A
,
subtract: n - m
,
lelt: i ≤ j < k
,
satisfiable_int_formula: satisfiable_int_formula(fmla)
,
exists: ∃x:A. B[x]
Lemmas referenced :
radd_wf,
req_witness,
int_seg_wf,
int_formula_prop_wf,
int_formula_prop_le_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_and_lemma,
intformle_wf,
itermConstant_wf,
itermVar_wf,
intformless_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_seg_cases,
false_wf,
int_seg_subtype,
int_seg_properties,
int_subtype_base,
subtype_base_sq,
decidable__equal_int,
length_of_nil_lemma,
length_of_cons_lemma,
length_wf,
nil_wf,
real_wf,
cons_wf,
radd-list_functionality,
iff_weakening_equal,
radd-as-radd-list,
true_wf,
squash_wf,
req_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
applyEquality,
thin,
lambdaEquality,
sqequalHypSubstitution,
imageElimination,
lemma_by_obid,
isectElimination,
hypothesisEquality,
equalityTransitivity,
hypothesis,
equalitySymmetry,
because_Cache,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
productElimination,
independent_functionElimination,
independent_pairFormation,
lambdaFormation,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
setElimination,
rename,
unionElimination,
instantiate,
cumulativity,
intEquality,
hypothesis_subsumption,
addEquality,
dependent_pairFormation,
int_eqEquality,
computeAll
Latex:
\mforall{}[a1,a2,b1,b2:\mBbbR{}]. ((a1 + b1) = (a2 + b2)) supposing ((a1 = a2) and (b1 = b2))
Date html generated:
2016_05_18-AM-06_51_00
Last ObjectModification:
2016_01_17-AM-01_46_23
Theory : reals
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