Nuprl Lemma : subtract-elim
∀[x,y:ℤ].  (x - y ~ x + (-y))
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
subtract: n - m
, 
add: n + m
, 
minus: -n
, 
int: ℤ
, 
sqequal: s ~ t
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uimplies: b supposing a
, 
all: ∀x:A. B[x]
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
exists: ∃x:A. B[x]
, 
false: False
, 
implies: P 
⇒ Q
, 
not: ¬A
, 
top: Top
, 
prop: ℙ
, 
sq_type: SQType(T)
, 
guard: {T}
Lemmas referenced : 
int_formula_prop_wf, 
int_term_value_minus_lemma, 
int_term_value_add_lemma, 
int_term_value_var_lemma, 
int_term_value_subtract_lemma, 
int_formula_prop_eq_lemma, 
int_formula_prop_not_lemma, 
itermMinus_wf, 
itermAdd_wf, 
itermVar_wf, 
itermSubtract_wf, 
intformeq_wf, 
intformnot_wf, 
satisfiable-full-omega-tt, 
decidable__equal_int, 
int_subtype_base, 
subtype_base_sq
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
thin, 
instantiate, 
lemma_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
because_Cache, 
independent_isectElimination, 
hypothesis, 
dependent_functionElimination, 
unionElimination, 
natural_numberEquality, 
dependent_pairFormation, 
lambdaEquality, 
int_eqEquality, 
hypothesisEquality, 
intEquality, 
isect_memberEquality, 
voidElimination, 
voidEquality, 
sqequalRule, 
computeAll, 
equalityTransitivity, 
equalitySymmetry, 
independent_functionElimination, 
sqequalAxiom
Latex:
\mforall{}[x,y:\mBbbZ{}].    (x  -  y  \msim{}  x  +  (-y))
Date html generated:
2016_05_14-PM-04_22_19
Last ObjectModification:
2016_01_14-PM-11_40_29
Theory : num_thy_1
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