### 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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