Nuprl Lemma : rminus_functionality
∀[x,y:ℝ]. -(x) = -(y) supposing x = y
Proof
Definitions occuring in Statement :
req: x = y,
rminus: -(x),
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,
req: x = y,
all: ∀x:A. B[x],
squash: ↓T,
prop: ℙ,
subtype_rel: A ⊆r B,
real: ℝ,
le: A ≤ B,
and: P ∧ Q,
true: True,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
rminus: -(x),
nat_plus: ℕ+,
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
le_wf,
squash_wf,
true_wf,
absval_sym,
subtract_wf,
rminus_wf,
iff_weakening_equal,
nat_plus_wf,
req_witness,
req_wf,
real_wf,
absval_wf,
nat_plus_properties,
decidable__equal_int,
less_than_wf,
satisfiable-full-omega-tt,
intformnot_wf,
intformeq_wf,
itermMinus_wf,
itermSubtract_wf,
itermVar_wf,
int_formula_prop_not_lemma,
int_formula_prop_eq_lemma,
int_term_value_minus_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
lambdaFormation,
hypothesis,
dependent_functionElimination,
thin,
hypothesisEquality,
applyEquality,
lambdaEquality,
imageElimination,
extract_by_obid,
isectElimination,
equalityTransitivity,
equalitySymmetry,
intEquality,
setElimination,
rename,
because_Cache,
sqequalRule,
productElimination,
natural_numberEquality,
imageMemberEquality,
baseClosed,
universeEquality,
independent_isectElimination,
independent_functionElimination,
isect_memberEquality,
hyp_replacement,
unionElimination,
dependent_set_memberEquality,
dependent_pairFormation,
int_eqEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}[x,y:\mBbbR{}]. -(x) = -(y) supposing x = y
Date html generated:
2016_10_26-AM-09_03_34
Last ObjectModification:
2016_07_12-AM-08_13_37
Theory : reals
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