Nuprl Lemma : rminus_functionality_wrt_rleq
∀[x,y:ℝ]. -(x) ≤ -(y) supposing x ≥ y
Proof
Definitions occuring in Statement :
rge: x ≥ y,
rleq: 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,
rleq: x ≤ y,
rnonneg: rnonneg(x),
all: ∀x:A. B[x],
le: A ≤ B,
and: P ∧ Q,
not: ¬A,
implies: P ⇒ Q,
false: False,
subtype_rel: A ⊆r B,
real: ℝ,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q),
itermConstant: "const",
req_int_terms: t1 ≡ t2,
top: Top,
rge: x ≥ y
Lemmas referenced :
less_than'_wf,
rsub_wf,
rminus_wf,
real_wf,
nat_plus_wf,
rge_wf,
radd-preserves-rleq,
radd_wf,
int-to-real_wf,
rmul_wf,
rleq_functionality,
real_term_polynomial,
itermSubtract_wf,
itermAdd_wf,
itermVar_wf,
itermMinus_wf,
itermConstant_wf,
real_term_value_const_lemma,
real_term_value_sub_lemma,
real_term_value_add_lemma,
real_term_value_var_lemma,
real_term_value_minus_lemma,
req-iff-rsub-is-0,
req_transitivity,
itermMultiply_wf,
real_term_value_mul_lemma,
radd_functionality,
req_weakening,
rmul-identity1,
req_inversion,
rminus-as-rmul
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
sqequalHypSubstitution,
lambdaEquality,
dependent_functionElimination,
thin,
hypothesisEquality,
productElimination,
independent_pairEquality,
because_Cache,
extract_by_obid,
isectElimination,
applyEquality,
hypothesis,
setElimination,
rename,
minusEquality,
natural_numberEquality,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
isect_memberEquality,
voidElimination,
independent_isectElimination,
computeAll,
int_eqEquality,
intEquality,
voidEquality
Latex:
\mforall{}[x,y:\mBbbR{}]. -(x) \mleq{} -(y) supposing x \mgeq{} y
Date html generated:
2017_10_03-AM-08_28_18
Last ObjectModification:
2017_07_28-AM-07_25_09
Theory : reals
Home
Index