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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