Nuprl Lemma : qlog-type_wf
∀[q,e:ℚ]. (qlog-type(q;e) ∈ Type)
Proof
Definitions occuring in Statement :
qlog-type: qlog-type(q;e),
rationals: ℚ,
uall: ∀[x:A]. B[x],
member: t ∈ T,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
qlog-type: qlog-type(q;e),
and: P ∧ Q,
implies: P ⇒ Q,
subtype_rel: A ⊆r B,
prop: ℙ,
nat: ℕ,
nat_plus: ℕ+,
all: ∀x:A. B[x],
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top
Lemmas referenced :
rationals_wf,
nat_plus_subtype_nat,
qless_wf,
le_wf,
int_formula_prop_wf,
int_formula_prop_less_lemma,
int_term_value_var_lemma,
int_term_value_subtract_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
intformless_wf,
itermVar_wf,
itermSubtract_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
nat_plus_properties,
subtract_wf,
qexp_wf,
qle_wf,
nat_plus_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
setEquality,
lemma_by_obid,
hypothesis,
productEquality,
functionEquality,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
natural_numberEquality,
applyEquality,
because_Cache,
dependent_set_memberEquality,
setElimination,
rename,
dependent_functionElimination,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll,
axiomEquality,
equalityTransitivity,
equalitySymmetry
Latex:
\mforall{}[q,e:\mBbbQ{}]. (qlog-type(q;e) \mmember{} Type)
Date html generated:
2016_05_15-PM-11_15_29
Last ObjectModification:
2016_01_16-PM-09_19_17
Theory : rationals
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