Nuprl Lemma : imax_strict_lb
∀[a,b,c:ℤ]. uiff(imax(a;b) < c;a < c ∧ b < c)
Proof
Definitions occuring in Statement :
imax: imax(a;b),
less_than: a < b,
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
and: P ∧ Q,
int: ℤ
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
squash: ↓T,
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},
cand: A c∧ B,
le: A ≤ B
Lemmas referenced :
and_wf,
less_than_wf,
member-less_than,
decidable__lt,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_constant_lemma,
int_term_value_subtract_lemma,
int_term_value_var_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
imax_wf,
decidable__le,
subtract_wf,
imax_lb
Rules used in proof :
cut,
lemma_by_obid,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
introduction,
natural_numberEquality,
productElimination,
independent_pairFormation,
independent_isectElimination,
dependent_functionElimination,
because_Cache,
unionElimination,
imageElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
computeAll,
independent_pairEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b,c:\mBbbZ{}]. uiff(imax(a;b) < c;a < c \mwedge{} b < c)
Date html generated:
2016_05_14-AM-07_22_07
Last ObjectModification:
2016_01_07-PM-04_00_37
Theory : int_2
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