Nuprl Lemma : decidable__equal-coordinate_name
∀x,y:Cname. Dec(x = y ∈ Cname)
Proof
Definitions occuring in Statement :
coordinate_name: Cname,
decidable: Dec(P),
all: ∀x:A. B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
coordinate_name: Cname,
all: ∀x:A. B[x],
member: t ∈ T,
uall: ∀[x:A]. B[x],
int_upper: {i...},
decidable: Dec(P),
or: P ∨ Q,
guard: {T},
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
implies: P ⇒ Q,
not: ¬A,
top: Top,
and: P ∧ Q,
prop: ℙ
Lemmas referenced :
equal_wf,
not_wf,
le_wf,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
itermConstant_wf,
intformle_wf,
decidable__le,
int_formula_prop_wf,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
int_upper_properties,
decidable__equal_int,
int_upper_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
lambdaFormation,
cut,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
natural_numberEquality,
hypothesis,
dependent_functionElimination,
setElimination,
rename,
hypothesisEquality,
unionElimination,
inlFormation,
independent_isectElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
sqequalRule,
independent_pairFormation,
computeAll,
dependent_set_memberEquality,
because_Cache,
inrFormation,
applyEquality,
setEquality,
independent_functionElimination
Latex:
\mforall{}x,y:Cname. Dec(x = y)
Date html generated:
2016_05_20-AM-09_28_03
Last ObjectModification:
2016_01_18-PM-04_58_49
Theory : cubical!sets
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