Nuprl Lemma : rminus-rminus-eq
∀[x:ℝ]. (-(-(x)) = x ∈ ℝ)
Proof
Definitions occuring in Statement :
rminus: -(x),
real: ℝ,
uall: ∀[x:A]. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
real: ℝ,
rminus: -(x),
member: t ∈ T,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
real_wf,
regular-int-seq_wf,
nat_plus_wf,
int_formula_prop_wf,
int_term_value_minus_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
itermMinus_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
nat_plus_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
cut,
equalitySymmetry,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
functionExtensionality,
sqequalRule,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[x:\mBbbR{}]. (-(-(x)) = x)
Date html generated:
2016_05_18-AM-06_51_12
Last ObjectModification:
2016_01_17-AM-01_46_04
Theory : reals
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