Nuprl Lemma : intlex-aux-reflexive
∀[l1,l2:ℤ List]. intlex-aux(l1;l2) = tt supposing l1 = l2 ∈ (ℤ List)
Proof
Definitions occuring in Statement :
intlex-aux: intlex-aux(l1;l2),
list: T List,
btrue: tt,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
int: ℤ,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
so_lambda: λ2x.t[x],
subtype_rel: A ⊆r B,
uimplies: b supposing a,
so_apply: x[s],
implies: P ⇒ Q,
intlex-aux: intlex-aux(l1;l2),
nil: [],
it: ⋅,
btrue: tt,
bool: 𝔹,
all: ∀x:A. B[x],
cons: [a / b],
so_lambda: λ2x y.t[x; y],
top: Top,
so_apply: x[s1;s2],
less_than: a < b,
and: P ∧ Q,
less_than': less_than'(a;b),
true: True,
squash: ↓T,
not: ¬A,
false: False,
prop: ℙ,
guard: {T},
sq_type: SQType(T)
Lemmas referenced :
list_induction,
equal-wf-base,
bool_wf,
list_subtype_base,
int_subtype_base,
list_wf,
it_wf,
subtype_rel_union,
unit_wf2,
spread_cons_lemma,
top_wf,
less_than_anti-reflexive,
less_than_wf,
subtype_base_sq,
and_wf,
equal_wf
Rules used in proof :
cut,
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
thin,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
intEquality,
sqequalRule,
lambdaEquality,
hypothesis,
baseApply,
closedConclusion,
baseClosed,
hypothesisEquality,
applyEquality,
because_Cache,
independent_isectElimination,
independent_functionElimination,
inlEquality,
voidEquality,
voidElimination,
lambdaFormation,
rename,
dependent_functionElimination,
isect_memberEquality,
int_eqReduceTrueSq,
lessCases,
sqequalAxiom,
independent_pairFormation,
natural_numberEquality,
imageMemberEquality,
imageElimination,
productElimination,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
hyp_replacement,
instantiate,
dependent_set_memberEquality,
applyLambdaEquality,
setElimination
Latex:
\mforall{}[l1,l2:\mBbbZ{} List]. intlex-aux(l1;l2) = tt supposing l1 = l2
Date html generated:
2017_09_29-PM-05_50_11
Last ObjectModification:
2017_07_26-PM-01_39_16
Theory : list_0
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