Nuprl Lemma : word-rel-length
∀[X:Type]. ∀[w1,w2:(X + X) List]. ||w2|| < ||w1|| supposing word-rel(X;w1;w2)
Proof
Definitions occuring in Statement :
word-rel: word-rel(X;w1;w2),
length: ||as||,
list: T List,
less_than: a < b,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
union: left + right,
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
word-rel: word-rel(X;w1;w2),
exists: ∃x:A. B[x],
and: P ∧ Q,
prop: ℙ,
true: True,
top: Top,
append: as @ bs,
all: ∀x:A. B[x],
so_lambda: so_lambda3,
so_apply: x[s1;s2;s3],
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
false: False,
implies: P ⇒ Q,
not: ¬A,
squash: ↓T,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
word-rel_wf,
member-less_than,
length_wf,
list_wf,
length-append,
list_ind_cons_lemma,
list_ind_nil_lemma,
length_of_cons_lemma,
length_of_nil_lemma,
decidable__lt,
satisfiable-full-omega-tt,
intformnot_wf,
intformless_wf,
itermAdd_wf,
itermVar_wf,
itermConstant_wf,
int_formula_prop_not_lemma,
int_formula_prop_less_lemma,
int_term_value_add_lemma,
int_term_value_var_lemma,
int_term_value_constant_lemma,
int_formula_prop_wf,
less_than_wf,
squash_wf,
true_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalHypSubstitution,
productElimination,
thin,
hypothesis,
extract_by_obid,
isectElimination,
cumulativity,
hypothesisEquality,
sqequalRule,
isect_memberEquality,
unionEquality,
independent_isectElimination,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
voidElimination,
voidEquality,
dependent_functionElimination,
addEquality,
unionElimination,
dependent_pairFormation,
lambdaEquality,
int_eqEquality,
intEquality,
computeAll,
applyEquality,
imageElimination,
imageMemberEquality,
baseClosed,
independent_functionElimination
Latex:
\mforall{}[X:Type]. \mforall{}[w1,w2:(X + X) List]. ||w2|| < ||w1|| supposing word-rel(X;w1;w2)
Date html generated:
2020_05_20-AM-08_21_49
Last ObjectModification:
2017_01_14-PM-04_46_23
Theory : free!groups
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