Nuprl Lemma : comparison-reflexive
∀[T:Type]. ∀cmp:comparison(T). ∀x:T. ((cmp x x) = 0 ∈ ℤ)
Proof
Definitions occuring in Statement :
comparison: comparison(T),
uall: ∀[x:A]. B[x],
all: ∀x:A. B[x],
apply: f a,
natural_number: $n,
int: ℤ,
universe: Type,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
comparison: comparison(T),
and: P ∧ Q,
decidable: Dec(P),
or: P ∨ Q,
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,
prop: ℙ
Lemmas referenced :
int_formula_prop_wf,
int_term_value_minus_lemma,
int_term_value_constant_lemma,
int_term_value_var_lemma,
int_formula_prop_eq_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermMinus_wf,
itermConstant_wf,
itermVar_wf,
intformeq_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__equal_int,
comparison_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
productElimination,
hypothesis,
hypothesisEquality,
lemma_by_obid,
dependent_functionElimination,
sqequalRule,
lambdaEquality,
axiomEquality,
because_Cache,
universeEquality,
unionElimination,
equalityTransitivity,
equalitySymmetry,
isectElimination,
natural_numberEquality,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidElimination,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}cmp:comparison(T). \mforall{}x:T. ((cmp x x) = 0)
Date html generated:
2016_05_14-PM-02_35_52
Last ObjectModification:
2016_01_15-AM-07_42_19
Theory : list_1
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