Nuprl Lemma : term-size-positive
∀[opr:Type]. ∀t:term(opr). (1 ≤ term-size(t))
Proof
Definitions occuring in Statement : 
term-size: term-size(t)
, 
term: term(opr)
, 
uall: ∀[x:A]. B[x]
, 
le: A ≤ B
, 
all: ∀x:A. B[x]
, 
natural_number: $n
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
all: ∀x:A. B[x]
, 
or: P ∨ Q
, 
exists: ∃x:A. B[x]
, 
and: P ∧ Q
, 
true: True
, 
le: A ≤ B
, 
less_than': less_than'(a;b)
, 
false: False
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
squash: ↓T
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
nat: ℕ
, 
uimplies: b supposing a
, 
guard: {T}
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
, 
lsum: Σ(f[x] | x ∈ L)
, 
bound-term: bound-term(opr)
, 
pi2: snd(t)
, 
bound-term-size: bound-term-size(bt)
, 
l_all: (∀x∈L.P[x])
, 
ge: i ≥ j 
, 
int_seg: {i..j-}
, 
lelt: i ≤ j < k
, 
decidable: Dec(P)
, 
satisfiable_int_formula: satisfiable_int_formula(fmla)
, 
so_lambda: λ2x.t[x]
, 
so_apply: x[s]
Lemmas referenced : 
term-cases, 
term_wf, 
istype-universe, 
term_size_var_lemma, 
istype-false, 
term_size_mkterm_lemma, 
le_wf, 
squash_wf, 
true_wf, 
istype-int, 
term-size_wf, 
istype-nat, 
subtype_rel_self, 
iff_weakening_equal, 
l_sum_nonneg, 
map_wf, 
bound-term_wf, 
less_than_wf, 
bound-term-size_wf, 
istype-less_than, 
non_neg_length, 
nat_wf, 
map_length, 
int_seg_properties, 
decidable__le, 
select_wf, 
length_wf, 
nat_properties, 
full-omega-unsat, 
intformand_wf, 
intformle_wf, 
itermConstant_wf, 
itermVar_wf, 
intformnot_wf, 
int_formula_prop_and_lemma, 
int_formula_prop_le_lemma, 
int_term_value_constant_lemma, 
int_term_value_var_lemma, 
int_formula_prop_not_lemma, 
int_formula_prop_wf, 
istype-le, 
length_wf_nat, 
int_seg_wf, 
lsum_wf, 
l_member_wf, 
itermAdd_wf, 
int_term_value_add_lemma
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation_alt, 
hypothesis, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
lambdaFormation_alt, 
dependent_functionElimination, 
unionElimination, 
productElimination, 
universeIsType, 
instantiate, 
universeEquality, 
natural_numberEquality, 
sqequalRule, 
Error :memTop, 
independent_pairFormation, 
applyEquality, 
lambdaEquality_alt, 
imageElimination, 
equalityTransitivity, 
equalitySymmetry, 
inhabitedIsType, 
because_Cache, 
imageMemberEquality, 
baseClosed, 
setElimination, 
rename, 
independent_isectElimination, 
independent_functionElimination, 
setEquality, 
closedConclusion, 
intEquality, 
setIsType, 
dependent_set_memberEquality_alt, 
applyLambdaEquality, 
approximateComputation, 
dependent_pairFormation_alt, 
int_eqEquality, 
voidElimination, 
addEquality
Latex:
\mforall{}[opr:Type].  \mforall{}t:term(opr).  (1  \mleq{}  term-size(t))
Date html generated:
2020_05_19-PM-09_54_01
Last ObjectModification:
2020_03_12-AM-10_54_11
Theory : terms
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