Nuprl Lemma : comparison-refl
∀[T:Type]. ∀cmp:comparison(T). Refl(T;x,y.0 ≤ (cmp x y))
Proof
Definitions occuring in Statement :
comparison: comparison(T),
refl: Refl(T;x,y.E[x; y]),
uall: ∀[x:A]. B[x],
le: A ≤ B,
all: ∀x:A. B[x],
apply: f a,
natural_number: $n,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
all: ∀x:A. B[x],
refl: Refl(T;x,y.E[x; y]),
comparison: comparison(T),
sq_stable: SqStable(P),
implies: P ⇒ Q,
and: P ∧ Q,
squash: ↓T,
le: A ≤ B,
not: ¬A,
false: False,
prop: ℙ,
decidable: Dec(P),
or: P ∨ Q,
uimplies: b supposing a,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
top: Top
Lemmas referenced :
int_formula_prop_wf,
int_term_value_minus_lemma,
int_formula_prop_eq_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_le_lemma,
int_formula_prop_not_lemma,
int_formula_prop_and_lemma,
itermMinus_wf,
intformeq_wf,
itermVar_wf,
itermConstant_wf,
intformle_wf,
intformnot_wf,
intformand_wf,
satisfiable-full-omega-tt,
decidable__le,
less_than'_wf,
comparison_wf,
sq_stable__le
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
lambdaFormation,
sqequalHypSubstitution,
setElimination,
thin,
rename,
lemma_by_obid,
isectElimination,
natural_numberEquality,
applyEquality,
hypothesisEquality,
hypothesis,
independent_functionElimination,
productElimination,
sqequalRule,
imageMemberEquality,
baseClosed,
imageElimination,
dependent_functionElimination,
lambdaEquality,
independent_pairEquality,
voidElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
because_Cache,
universeEquality,
unionElimination,
independent_isectElimination,
dependent_pairFormation,
int_eqEquality,
intEquality,
isect_memberEquality,
voidEquality,
independent_pairFormation,
computeAll
Latex:
\mforall{}[T:Type]. \mforall{}cmp:comparison(T). Refl(T;x,y.0 \mleq{} (cmp x y))
Date html generated:
2016_05_14-PM-02_38_46
Last ObjectModification:
2016_01_15-AM-07_39_11
Theory : list_1
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