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
Home
Index