Nuprl Lemma : imax_strict_ub
∀a,b,c:ℤ. (a < imax(b;c) ⇐⇒ a < b ∨ a < c)
Proof
Definitions occuring in Statement :
imax: imax(a;b),
less_than: a < b,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q,
int: ℤ
Definitions unfolded in proof :
all: ∀x:A. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q,
uall: ∀[x:A]. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ
Lemmas referenced :
or_wf,
imax_wf,
int_formula_prop_wf,
int_term_value_constant_lemma,
int_term_value_add_lemma,
int_formula_prop_le_lemma,
int_formual_prop_imp_lemma,
int_term_value_var_lemma,
int_formula_prop_less_lemma,
int_formula_prop_or_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermConstant_wf,
itermAdd_wf,
intformle_wf,
intformimplies_wf,
itermVar_wf,
intformless_wf,
intformor_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__lt,
less_than_wf,
decidable__or,
imax_ub
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
addEquality,
hypothesisEquality,
natural_numberEquality,
hypothesis,
productElimination,
independent_pairFormation,
sqequalRule,
isectElimination,
independent_functionElimination,
because_Cache,
unionElimination,
imageElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
computeAll
Latex:
\mforall{}a,b,c:\mBbbZ{}. (a < imax(b;c) \mLeftarrow{}{}\mRightarrow{} a < b \mvee{} a < c)
Date html generated:
2016_05_14-AM-07_22_05
Last ObjectModification:
2016_01_07-PM-04_00_38
Theory : int_2
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