Nuprl Lemma : q-ceil_functionality
∀[a,b:ℚ]. q-ceil(a) ≤ q-ceil(b) supposing a ≤ b
Proof
Definitions occuring in Statement :
q-ceil: q-ceil(r),
qle: r ≤ s,
rationals: ℚ,
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,
uiff: uiff(P;Q),
and: P ∧ Q,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
prop: ℙ,
subtype_rel: A ⊆r B,
guard: {T}
Lemmas referenced :
qless_irreflexivity,
qless_transitivity_2_qorder,
qsub_wf,
rationals_wf,
qle_wf,
int-subtype-rationals,
qle_witness,
qsub-sub,
int_formula_prop_wf,
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,
itermConstant_wf,
itermSubtract_wf,
itermVar_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
subtract_wf,
decidable__le,
q-ceil-property,
q-ceil_wf,
qle-int
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
hypothesis,
productElimination,
independent_isectElimination,
dependent_functionElimination,
unionElimination,
natural_numberEquality,
because_Cache,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
applyEquality,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[a,b:\mBbbQ{}]. q-ceil(a) \mleq{} q-ceil(b) supposing a \mleq{} b
Date html generated:
2016_05_15-PM-11_35_09
Last ObjectModification:
2016_01_16-PM-09_12_47
Theory : rationals
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