Nuprl Lemma : rless_irreflexivity
∀[e:ℝ]. False supposing e < e
Proof
Definitions occuring in Statement :
rless: x < y,
real: ℝ,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
false: False,
rless: x < y,
sq_exists: ∃x:{A| B[x]},
nat_plus: ℕ+,
less_than: a < b,
squash: ↓T,
and: P ∧ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
implies: P ⇒ Q,
not: ¬A,
all: ∀x:A. B[x],
top: Top,
prop: ℙ
Lemmas referenced :
real_wf,
rless_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_term_value_add_lemma,
int_formula_prop_less_lemma,
itermConstant_wf,
itermVar_wf,
itermAdd_wf,
intformless_wf,
satisfiable-full-omega-tt,
nat_plus_properties
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
hypothesisEquality,
hypothesis,
imageElimination,
productElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
dependent_functionElimination,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
because_Cache,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[e:\mBbbR{}]. False supposing e < e
Date html generated:
2016_05_18-AM-07_10_00
Last ObjectModification:
2016_01_17-AM-01_50_55
Theory : reals
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