Nuprl Lemma : rcp_functionality
∀[a1,b1,a2,b2:ℝ^3]. (req-vec(3;(a1 x b1);(a2 x b2))) supposing (req-vec(3;b1;b2) and req-vec(3;a1;a2))
Proof
Definitions occuring in Statement :
rcp: (a x b),
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
natural_number: $n
Definitions unfolded in proof :
rcp: (a x b),
req-vec: req-vec(n;x;y),
real-vec: ℝ^n,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
all: ∀x:A. B[x],
int_seg: {i..j-},
decidable: Dec(P),
or: P ∨ Q,
sq_type: SQType(T),
implies: P ⇒ Q,
guard: {T},
select: L[n],
cons: [a / b],
subtract: n - m,
lelt: i ≤ j < k,
and: P ∧ Q,
not: ¬A,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
top: Top,
prop: ℙ,
uiff: uiff(P;Q),
rev_uimplies: rev_uimplies(P;Q)
Lemmas referenced :
decidable__equal_int,
subtype_base_sq,
int_subtype_base,
int_seg_properties,
int_seg_subtype_special,
int_seg_cases,
full-omega-unsat,
intformand_wf,
intformless_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
istype-int,
int_formula_prop_and_lemma,
istype-void,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_wf,
int_seg_wf,
req_witness,
select_wf,
real_wf,
cons_wf,
rsub_wf,
rmul_wf,
decidable__le,
intformnot_wf,
int_formula_prop_not_lemma,
decidable__lt,
istype-le,
istype-less_than,
nil_wf,
length_of_cons_lemma,
length_of_nil_lemma,
itermAdd_wf,
int_term_value_add_lemma,
req_wf,
req_weakening,
req_functionality,
rsub_functionality,
rmul_functionality
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
isect_memberFormation_alt,
introduction,
cut,
lambdaFormation_alt,
extract_by_obid,
sqequalHypSubstitution,
dependent_functionElimination,
thin,
setElimination,
rename,
hypothesisEquality,
hypothesis,
natural_numberEquality,
unionElimination,
instantiate,
isectElimination,
cumulativity,
intEquality,
independent_isectElimination,
because_Cache,
independent_functionElimination,
equalityTransitivity,
equalitySymmetry,
hypothesis_subsumption,
productElimination,
approximateComputation,
dependent_pairFormation_alt,
lambdaEquality_alt,
int_eqEquality,
isect_memberEquality_alt,
voidElimination,
independent_pairFormation,
universeIsType,
applyEquality,
dependent_set_memberEquality_alt,
productIsType,
addEquality,
functionIsTypeImplies,
inhabitedIsType,
functionIsType,
isectIsTypeImplies
Latex:
\mforall{}[a1,b1,a2,b2:\mBbbR{}\^{}3].
(req-vec(3;(a1 x b1);(a2 x b2))) supposing (req-vec(3;b1;b2) and req-vec(3;a1;a2))
Date html generated:
2019_10_30-AM-08_56_23
Last ObjectModification:
2018_12_11-AM-10_54_48
Theory : reals
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