Nuprl Lemma : rminus-rminus
∀[x:ℝ]. (-(-(x)) = x)
Proof
Definitions occuring in Statement :
req: x = y,
rminus: -(x),
real: ℝ,
uall: ∀[x:A]. B[x]
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
real: ℝ,
rminus: -(x),
nat_plus: ℕ+,
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,
guard: {T}
Lemmas referenced :
real_wf,
req_witness,
req_inversion,
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,
rminus_wf,
req_weakening
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
independent_isectElimination,
setElimination,
rename,
dependent_set_memberEquality,
functionExtensionality,
sqequalRule,
dependent_functionElimination,
because_Cache,
unionElimination,
natural_numberEquality,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll,
independent_functionElimination
Latex:
\mforall{}[x:\mBbbR{}]. (-(-(x)) = x)
Date html generated:
2016_05_18-AM-06_51_09
Last ObjectModification:
2016_01_17-AM-01_46_06
Theory : reals
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