Nuprl Lemma : qmax_ub
∀a,b,c:ℚ. (a ≤ qmax(b;c) ⇐⇒ (a ≤ b) ∨ (a ≤ c))
Proof
Definitions occuring in Statement :
qmax: qmax(x;y),
qle: r ≤ s,
rationals: ℚ,
all: ∀x:A. B[x],
iff: P ⇐⇒ Q,
or: P ∨ Q
Definitions unfolded in proof :
all: ∀x:A. B[x],
qmax: qmax(x;y),
member: t ∈ T,
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
guard: {T},
or: P ∨ Q,
prop: ℙ,
rev_implies: P ⇐ Q,
uimplies: b supposing a,
true: True,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
squash: ↓T
Lemmas referenced :
rationals_wf,
q_le_wf,
bool_wf,
equal-wf-T-base,
assert_wf,
qle_wf,
qle_transitivity_qorder,
or_wf,
bnot_wf,
not_wf,
uiff_transitivity2,
eqtt_to_assert,
assert-q_le-eq,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
squash_wf,
true_wf,
equal_wf,
qle_complement_qorder,
qless_transitivity_1_qorder,
qle_weakening_lt_qorder
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
introduction,
extract_by_obid,
hypothesis,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
baseClosed,
because_Cache,
independent_pairFormation,
sqequalRule,
inrFormation,
unionElimination,
independent_isectElimination,
natural_numberEquality,
inlFormation,
equalityElimination,
independent_functionElimination,
productElimination,
applyEquality,
lambdaEquality,
imageElimination,
universeEquality,
imageMemberEquality,
dependent_functionElimination
Latex:
\mforall{}a,b,c:\mBbbQ{}. (a \mleq{} qmax(b;c) \mLeftarrow{}{}\mRightarrow{} (a \mleq{} b) \mvee{} (a \mleq{} c))
Date html generated:
2018_05_21-PM-11_54_55
Last ObjectModification:
2017_07_26-PM-06_45_51
Theory : rationals
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